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<a href="arith__theorem__producer__old_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*****************************************************************************/</span><span class="comment"></span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">/*!</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * \file arith_theorem_producer_old.h</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * \brief TRUSTED implementation of arithmetic proof rules</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * Author: Vijay Ganesh, Sergey Berezin</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * Created: Dec 13 02:09:04 GMT 2002</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * and its documentation for any purpose is hereby granted without</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * LICENSE file provided with this distribution.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">/*****************************************************************************/</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#ifndef _cvc3__arith_theorem_producer_old_h_</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor"></span><span class="preprocessor">#define _cvc3__arith_theorem_producer_old_h_</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include "<a class="code" href="arith__proof__rules_8h.html" title="Arithmetic proof rules.">arith_proof_rules.h</a>"</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include "<a class="code" href="theorem__producer_8h.html">theorem_producer.h</a>"</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include "<a class="code" href="theory__arith__old_8h.html">theory_arith_old.h</a>"</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="keyword">namespace </span>CVC3 {</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a name="l00031"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html"> 31</a></span>  <span class="keyword">class </span><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html">ArithTheoremProducerOld</a>: <span class="keyword">public</span> <a class="code" href="classCVC3_1_1ArithProofRules.html">ArithProofRules</a>, <span class="keyword">public</span> <a class="code" href="classCVC3_1_1TheoremProducer.html">TheoremProducer</a> {</div>
<div class="line"><a name="l00032"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466"> 32</a></span>  <a class="code" href="classCVC3_1_1TheoryArithOld.html">TheoryArithOld</a>* <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">d_theoryArith</a>;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keyword">private</span>:<span class="comment"></span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"> /*! \name Auxiliary functions for eqElimIntRule()</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> * Methods that compute the subterms used in eqElimIntRule()</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"> *@{</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> */</span><span class="comment"></span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> //! Compute the special modulus: i - m*floor(i/m+1/2)</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"></span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a0f531ca3d0d71a1872e1519aeafa7700" title="Compute the special modulus: i - m*floor(i/m+1/2)">modEq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& i, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m);<span class="comment"></span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"> //! Create the term 't'. See eqElimIntRule().</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"></span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a312dc8f65e3f19567e078035d1c67228" title="Create the term 't'. See eqElimIntRule().">create_t</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& eqn);<span class="comment"></span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> //! Create the term 't2'. See eqElimIntRule().</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment"></span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a1e069e289a008b1becbd5aef9afdd386" title="Create the term 't2'. See eqElimIntRule().">create_t2</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& lhs, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& rhs, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t);<span class="comment"></span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment"> //! Create the term 't3'. See eqElimIntRule().</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment"></span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a7458e7bd26ab3c181402534228ddbcc0" title="Create the term 't3'. See eqElimIntRule().">create_t3</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& lhs, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& rhs, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t);<span class="comment"></span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment"> /*! @brief Takes sum = a_0 + a_1*x_1+...+a_n*x_n and returns the</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment"> * vector of similar monomials (in 'summands') with coefficients</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment"> * mod(a_i, m). If divide flag is true, the coefficients will be</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"> * mod(a_i,m)/m.</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8634bedfcede10ab17339fde0a72e5d6" title="Takes sum = a_0 + a_1*x_1+...+a_n*x_n and returns the vector of similar monomials (in 'summands') wit...">sumModM</a>(std::vector<Expr>& summands, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sum,</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& divisor);</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a9551aaeb071bd9c2b5703f69c2243e14" title="Compute the special modulus: i - m*floor(i/m+1/2)">monomialModM</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e,</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& divisor);</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a3d81fdb3d2ac10bfc3f2c0d73a5258e1" title="Compute the special modulus: i - m*floor(i/m+1/2)">sumMulF</a>(std::vector<Expr>& summands, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sum,</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& divisor);</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a2e2582c11f6547ed6faefaec6c9142f9" title="Compute the special modulus: i - m*floor(i/m+1/2)">monomialMulF</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e,</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& divisor);<span class="comment"></span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"> //! Compute floor(i/m+1/2) + mod(i,m)</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment"></span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ad7af04a277cf5337c02182ee9bf055a4" title="Compute floor(i/m+1/2) + mod(i,m)">f</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& i, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a77f3c348c3b6566fbae5c9750d568b9c" title="Compute the special modulus: i - m*floor(i/m+1/2)">substitute</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& term, <a class="code" href="classCVC3_1_1ExprMap.html">ExprMap<Expr></a>& eMap);</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae2174305ea66a5df62101bce0ada8d04" title="Compute the special modulus: i - m*floor(i/m+1/2)">getLeaves</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e, std::set<Rational>& s, <a class="code" href="classCVC3_1_1ExprHashMap.html">ExprHashMap<bool></a>& cache);<span class="comment"></span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment"> /*@}*/</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">public</span>:<span class="comment"></span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment"> //! Constructor</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4896b0d01e30e02300f74b9ae6b4d9d4"> 66</a></span> <span class="comment"></span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4896b0d01e30e02300f74b9ae6b4d9d4" title="Constructor.">ArithTheoremProducerOld</a>(<a class="code" href="classCVC3_1_1TheoremManager.html">TheoremManager</a>* tm, <a class="code" href="classCVC3_1_1TheoryArithOld.html">TheoryArithOld</a>* theoryArith):</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <a class="code" href="classCVC3_1_1TheoremProducer.html">TheoremProducer</a>(tm), <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">d_theoryArith</a>(theoryArith) { }</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment"></span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"> //! Create Expr from Rational (for convenience)</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8e7bf5bdb1872df7f21920c64a37c612"> 70</a></span> <span class="comment"></span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8e7bf5bdb1872df7f21920c64a37c612" title="Create Expr from Rational (for convenience)">rat</a>(<a class="code" href="classCVC3_1_1Rational.html">Rational</a> r) { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1TheoremProducer.html#a1b706238281ad141a57363a6890f14a5">d_em</a>-><a class="code" href="group__EM__Priv.html#ga18423a42ce6557dc33287d3979ccc3c6">newRatExpr</a>(r); }</div>
<div class="line"><a name="l00071"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ab22e2bf40e2473ab9dc34097c28a46a3"> 71</a></span>  <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ab22e2bf40e2473ab9dc34097c28a46a3">realType</a>() { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#a03fa81194322b92c488033695bec7204">realType</a>(); }</div>
<div class="line"><a name="l00072"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a520ba37f3cc4129559fc32289a027b82"> 72</a></span>  <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a520ba37f3cc4129559fc32289a027b82">intType</a>() { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#ad3e47bba6c50745ad194cf273aa1d146">intType</a>(); }<span class="comment"></span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"> //! Construct the dark shadow expression representing lhs <= rhs</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a9437ab7589a35fa490136b4b917ad244"> 74</a></span> <span class="comment"></span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a9437ab7589a35fa490136b4b917ad244" title="Construct the dark shadow expression representing lhs <= rhs.">darkShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& lhs, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& rhs) {</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#abee62d97b0c60a1a44b7ede3c60b11b6" title="Construct the dark shadow expression representing lhs <= rhs.">darkShadow</a>(lhs, rhs);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  }<span class="comment"></span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> //! Construct the gray shadow expression representing c1 <= v - e <= c2</span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"></span><span class="comment"> /*! Alternatively, v = e + i for some i s.t. c1 <= i <= c2</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965"> 80</a></span>  <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& v, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e,</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c2) {</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#ae7d59b8b9bff1ae3cbb1b67a0baa3463" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>(v, e, c1, c2);</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  }</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment"></span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment"> ////////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment"></span> <span class="comment">// Canonization rules</span><span class="comment"></span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"> ////////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"></span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="comment">// ==> x = 1 * x</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aebcc9153d9e9bfff3678c271674a6053" title="==> e = 1 * e">varToMult</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">// ==> -(e) = (-1) * e</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8165eb2a8fea70e0d1d2c8ebb1358855" title="==> -(e) = (-1) * e">uMinusToMult</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="comment">// ==> x - y = x + (-1) * y</span></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae3458f7b381a95e124e3204ed66904ef" title="==> x - y = x + (-1) * y">minusToPlus</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& y);</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="comment">// Rule for unary minus: it just converts it to division by -1,</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a693a5043cf100f13390b358290940dd5" title="-(e) ==> e / (-1); takes 'e'">canonUMinusToDivide</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">// Rules for division by constant 'd'</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="comment">// (c) / d ==> (c/d), takes c and d</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a237d508b95295db21e9ce21172d4366a" title="(c) / d ==> (c/d), takes c and d">canonDivideConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& d);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="comment">// (c * x) / d ==> (c/d) * x, takes (c*x) and d</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aea8367eb1c88d26b83aea3e5e63f66db" title="(c * x) / d ==> (c/d) * x, takes (c*x) and d">canonDivideMult</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& cx, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& d);</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="comment">// (+ c ...)/d ==> push division to all the coefficients.</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="comment">// The result is not canonical, but canonizing the summands will</span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// make it canonical.</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="comment">// Takes (+ c ...) and d</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a844e1fe500be8d1c083ddf6c06fcc85c" title="(+ c ...)/d ==> push division to all the coefficients.">canonDividePlus</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& d);</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="comment">// x / d ==> (1/d) * x, takes x and d</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#af79a13a84e24d58135d13d7520726134" title="x / d ==> (1/d) * x, takes x and d">canonDivideVar</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e2);</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="comment">// Canon Rules for multiplication</span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="comment">// TODO Deepak:</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">// t1 * t2 where t1 and t2 are canonized expressions, i.e. it can be a</span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="comment">// 1) Rational constant</span></div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// 2) Arithmetic Leaf (var or term from another theory)</span></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// 3) (POW rational leaf)</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="comment">// 4) (MULT rational mterm'_1 ...) where each mterm' is of type (2) or (3)</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="comment">// 5) (PLUS rational sterm_1 sterm_2 ...) where each sterm is of</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// type (2) or (3) or (4)</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> </div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keyword">static</span> <span class="keywordtype">bool</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ac6cae811b7bab0f2fc9aa62b94b461fd">greaterthan</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> &, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> &);</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aeebe92e51ed9f4f65fc949c66d240a1c">simplifiedMultExpr</a>(std::vector<Expr> & mulKids);</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4fe68827d0fd6cdccac139bc55416cb8">canonMultConstMult</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & c, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e);</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aa9f22909a2df31e9d59a96afecfa11dd">canonMultConstPlus</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2);</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a5840677a1efc3ab4ef21840d57654c5f">canonMultPowPow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2);</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae7bb027487c9e8312c4ca194ecfd379d">canonMultPowLeaf</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2);</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a71d7308e50c892d691d504397f5a92c8">canonMultLeafLeaf</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2);</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a040ec808dbbe743d9b138bfae33d24fc">canonMultLeafOrPowMult</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2);</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aad39a4a6b01790e883d49e03e3b513a9">canonCombineLikeTerms</a>(<span class="keyword">const</span> std::vector<Expr> & sumExprs);</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#acf0ff17451a851136910015ea515ac2f">canonMultLeafOrPowOrMultPlus</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2);</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae39478b27e22eee4837e7a132301b31a">canonMultPlusPlus</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2);</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ad7982dec66d9ebd08596c5b7d352604b">canonMultMtermMterm</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4a213b741317120ee84b6e61f50e484f" title="Canonize (PLUS t1 ... tn)">canonPlus</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a7696b12b3bc3ab04fdbf284a9466364a">canonInvertConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e);</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#acd60e50d112e88d021974c0b70956db6">canonInvertLeaf</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e);</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ad02b7e86f0f0edef419c4fe2adc74c99">canonInvertPow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e);</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a776468ac8d047b43cb460c9b3c600293">canonInvertMult</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e);</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a67391e426738cbd4a15f6fbc5b2d19e1" title="==> 1/e = e' where e' is canonical; takes e.">canonInvert</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e);</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"></span></div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment"> * Transform e = (SUM r t1 ... tn) @ 0 into (SUM t1 ... tn) @ -r. The first</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment"> * sum term (r) must be a rational and t1 ... tn terms must be canonised.</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment"> * @param e the expression to transform</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment"> * @return rewrite theorem representing the transformation</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a2b44fabb65bb6748259aee8959be465e">moveSumConstantRight</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment"></span></div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment"> /** e[0]/e[1] ==> e[0]*(e[1])^-1 */</span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aec48ed7710110960c6f87e6946500494">canonDivide</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e);</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"></span></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment"> /** Multiply out the operands of the multiplication (each of them is expected to be canonised */</span></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a50819c4cc053538490a2cbb535edf39d">canonMult</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e);</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> </div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="comment">// t*c ==> c*t, takes constant c and term t</span></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a70d0d0fa8c08582a17399c0570812afa" title="t*c ==> c*t, takes constant c and term t">canonMultTermConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t);</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="comment">// t1*t2 ==> Error, takes t1 and t2 where both are non-constants</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a10ed8952ec021d78cf1bc8b60e6634c6" title="t1*t2 ==> Error, takes t1 and t2 where both are non-constants">canonMultTerm1Term2</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t2);</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="comment">// 0*t ==> 0, takes 0*t</span></div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#af62a070ed7a3a326db5b121b282bd47c" title="0*t ==> 0, takes 0*t">canonMultZero</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="comment">// 1*t ==> t, takes 1*t</span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#abc03e832be081de0ca6f7f4e905e0f4f" title="1*t ==> t, takes 1*t">canonMultOne</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="comment">// c1*c2 ==> c', takes constant c1*c2</span></div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a3c1740f98f0ac4952c8d7a721767535e" title="c1*c2 ==> c', takes constant c1*c2">canonMultConstConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c2);</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">// c1*(c2*t) ==> c'*t, takes c1 and c2 and t</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8e0a636c4ee9bb70b8f36ee3f6acab49" title="c1*(c2*t) ==> c'*t, takes c1 and c2 and t">canonMultConstTerm</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c2, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>&t);</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="comment">// c1*(+ c2 v1 ...) ==> (+ c' c1v1 ...), takes c1 and the sum</span></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a5892d8574e2787b95005211cf0517952" title="c1*(+ c2 v1 ...) ==> (+ c' c1v1 ...), takes c1 and the sum">canonMultConstSum</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sum);</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="comment">// c^n = c' (compute the constant power expression)</span></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a7b083f1e452bd42475d9f0b313651fac" title="c^n = c' (compute the constant power expression)">canonPowConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& <a class="code" href="namespaceCVC3.html#a28fc84bed3f9bc91ca9967de0f9cfa00" title="Raise 'base' into the power of 'pow' (pow must be an integer)">pow</a>);</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> </div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="comment">// Rules for addition</span></div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="comment">// flattens the input. accepts a PLUS expr</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aba0cab7c4879b336dfac9cd1673be1c8" title="flattens the input. accepts a PLUS expr">canonFlattenSum</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="comment">// Rules for addition</span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="comment">// combine like terms. accepts a flattened PLUS expr</span></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a7f2a1a065eac005fa6b47c32040d9401" title="combine like terms. accepts a flattened PLUS expr">canonComboLikeTerms</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> </div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="comment">// 0 = (* e1 e2 ...) <=> 0 = e1 OR 0 = e2 OR ...</span></div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ad73622cdec4a472af97d68de6716fe0a">multEqZero</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr);</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> </div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="comment">// 0 = (^ c x) <=> false if c <=0</span></div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="comment">// <=> 0 = x if c > 0</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a9cc96dbb9ae7fa063146b9924f51fe68">powEqZero</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr);</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> </div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="comment">// x^n = y^n <=> x = y (if n is odd)</span></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="comment">// x^n = y^n <=> x = y OR x = -y (if n is even)</span></div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aeed414c650deb9b1e619ffb8f3266ea4">elimPower</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr);</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> </div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="comment">// x^n = c <=> x = root (if n is odd and root^n = c)</span></div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="comment">// x^n = c <=> x = root OR x = -root (if n is even and root^n = c)</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a2483c968c6a4d7f8ae63595c839b70f2">elimPowerConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& root);</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> </div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="comment">// x^n = c <=> false (if n is even and c is negative)</span></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afe5f71b9fdeb8be95e0e71e94df0b598">evenPowerEqNegConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr);</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> </div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="comment">// x^n = c <=> false (if x is an integer and c is not a perfect n power)</span></div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a75a67906db6381d408ea1a9830c36cf7">intEqIrrational</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="namespaceCVC3.html#a8b193cc1fee34cb43707171b2ae6471e">isInt</a>);</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> </div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="comment">// e[0] kind e[1] <==> true when e[0] kind e[1],</span></div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="comment">// false when e[0] !kind e[1], for constants only</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aefea69c7f808394db447b9ed658c59fa" title="e0 @ e1 <==> true | false, where @ is {=,<,<=,>,>=}">constPredicate</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> </div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">// e[0] kind e[1] <==> 0 kind e[1] - e[0]</span></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a088b20af694e737e1c7ff12d2ff74d7c" title="e[0] @ e[1] <==> 0 @ e[1] - e[0], where @ is {=,<,<=,>,>=}">rightMinusLeft</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> </div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="comment">// e[0] kind e[1] <==> e[0] - e[1] kind 0</span></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a36301e14b9eb42fc9842a3a7f60f8b17" title="e[0] @ e[1] <==> e[0] - e[1] @ 0, where @ is {=,<,<=,>,>=}">leftMinusRight</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> </div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="comment">// x kind y <==> x + z kind y + z</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a35577ad70c513422af5cbfca00cde1e2" title="x @ y <==> x + z @ y + z, where @ is {=,<,<=,>,>=} (given as 'kind')">plusPredicate</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x,</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& y,</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& z, <span class="keywordtype">int</span> kind);</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> </div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="comment">// x = y <==> x * z = y * z</span></div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aeb54d03f4672718b7de6160a88bf33cb" title="x = y <==> x * z = y * z, where z is a non-zero constant">multEqn</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& y, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& z);</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="comment">// x = y <==> z=0 OR x * 1/z = y * 1/z</span></div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a16c7325daba5b9e8cea7284fafaa5382">divideEqnNonConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& y, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& z);</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span> </div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="comment">// if z is +ve, return e[0] LT|LE|GT|GE e[1] <==> e[0]*z LT|LE|GT|GE e[1]*z</span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="comment">// if z is -ve, return e[0] LT|LE|GT|GE e[1] <==> e[1]*z LT|LE|GT|GE e[0]*z</span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aa425318a5846e14a94b2a3a34bb99b6d" title="Multiplying inequation by a non-zero constant.">multIneqn</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& z);</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="comment">// x = y ==> x <= y and x >= y</span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8edb275846dc5d938d3a8716436f0e1e" title="x = y ==> x <= y and x >= y">eqToIneq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span> </div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="comment">// "op1 GE|GT op2" <==> op2 LE|LT op1</span></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a86c578d9592d6782d2224118b755e0fa" title=""op1 GE|GT op2" <==> op2 LE|LT op1">flipInequality</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> </div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">// NOT (op1 LT op2) <==> (op1 GE op2)</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">// NOT (op1 LE op2) <==> (op1 GT op2)</span></div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="comment">// NOT (op1 GT op2) <==> (op1 LE op2)</span></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="comment">// NOT (op1 GE op2) <==> (op1 LT op2)</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a0b1fba36612db00956767d73bb1b6623" title="Propagating negation over <,<=,>,>=.">negatedInequality</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> </div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8f7858787d55442d57e5924dd232f842" title="Real shadow: a <(=) t, t <(=) b ==> a <(=) b.">realShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& alphaLTt, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLTbeta);</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a5033cb7a4be3d2e9bc1cd60582482c5f" title="alpha <= t <= alpha ==> t = alpha">realShadowEq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& alphaLEt, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLEalpha);</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae2869b5a206710a6c890d81ded080838" title="Finite interval for integers: a <= t <= a + c ==> G(t, a, 0, c)">finiteInterval</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& aLEt, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLEac,</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isInta, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntt);</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span> </div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a07e973f55e9daf1def982c84c3a078b1" title="Dark & Gray shadows when a <= b.">darkGrayShadow2ab</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& betaLEbx,</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& axLEalpha,</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntAlpha,</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntBeta,</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>);</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> </div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae27df6e46accf919b67dda1cb914c160" title="Dark & Gray shadows when b <= a.">darkGrayShadow2ba</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& betaLEbx,</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& axLEalpha,</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntAlpha,</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntBeta,</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>);</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a0b28ed8d0e2ef812bcfc8bba931e46cd">expandDarkShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a9437ab7589a35fa490136b4b917ad244" title="Construct the dark shadow expression representing lhs <= rhs.">darkShadow</a>);</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a273501b582758aca3ebabe6bd3ce83e4" title="GRAY_SHADOW(v, e, c, c) ==> v=e+c.">expandGrayShadow0</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a7fa5dbc59e8ce9a4315373092329a029" title="G(x, e, c1, c2) ==> (G1 or G2) and (!G1 or !G2)">splitGrayShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a0d76b8569909514e1f6a392a3778c04b">splitGrayShadowSmall</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a0e43921a028cfe58d5b50acd0c4a70ed" title="G(x, e, c1, c2) ==> e+c1 <= x AND x <= e+c2.">expandGrayShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae8c25031e88732d3259cd8e33d75e094" title="Optimized rules: GRAY_SHADOW(a*x, c, c1, c2) ==> [expansion].">expandGrayShadowConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a04d45720968a5ff4ccd6411413bd826e" title="|- G(ax, c, c1, c2) ==> |- G(x, 0, ceil((c1+c)/a), floor((c2+c)/a))">grayShadowConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& g);</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="comment"></span></div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="comment"> //! Implements j(c,b,a)</span></div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="comment"></span><span class="comment"> /*! accepts 3 integers a,b,c and returns</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment"> * (b > 0)? (c+b) mod a : (a - (c+b)) mod a</span></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#abd378d8d5a434e8df4809239bebc22fa" title="Implements j(c,b,a)">constRHSGrayShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c,</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& b,</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& a);</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> </div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a0ce54f8c725be25a6f6b11c7fbdc5321">lessThanToLE</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& less, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntLHS,</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS, <span class="keywordtype">bool</span> changeRight);</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span> </div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ab872ead63494b4afa6571e61a5cdd977">lessThanToLERewrite</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ineq, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntLHS,</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS, <span class="keywordtype">bool</span> changeRight);</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> </div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> </div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a99692dc40111d3082e7c583590c32188">intVarEqnConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& eqn, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>);</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#adc3a59f76832fd2671407c85b4b721a5">IsIntegerElim</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>);</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> </div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a85fd2ee0f7126d421fb53f4823ec8e77" title="Equality elimination rule for integers: See the detailed description for explanations.">eqElimIntRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& eqn, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>,</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keyword">const</span> std::vector<Theorem>& isIntVars);</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span> </div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a5ef5359db9aa12e8d196f7a39fc0fb55" title="return e <=> TRUE/FALSE for e == IS_INTEGER(c), where c is a constant">isIntConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> </div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a0a3f404013d038207a13103500e09c99">equalLeaves1</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae1820f8d68e98363139d77deae464f4f">equalLeaves2</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8e8ce7a2f17e5a855985bd0abfac6f12">equalLeaves3</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a24c874d01ca341845373cd41851a5a1b">equalLeaves4</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> </div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae723d1459d8c6f797ec08451f80f0798" title="x /= y ==> (x < y) OR (x > y)">diseqToIneq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& diseq);</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> </div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a3a3dd2d9c47ec607c816a9004c3659a5">dummyTheorem</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span> </div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aeb6d93e58c5c069ecbea38d013cbcf3e">oneElimination</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x);</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span> </div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aa71bcce02e1c1ce0d6ae588b4f341e4a">clashingBounds</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& lowerBound, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& upperBound);</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span> </div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a582df53749ebc6fd4011c614ff767181">addInequalities</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm2);</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a582df53749ebc6fd4011c614ff767181">addInequalities</a>(<span class="keyword">const</span> std::vector<Theorem>& thms);</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span> </div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a08879e8160aca1424c12e098f78df383">implyWeakerInequality</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2);</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> </div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a3597b8abdecd9f22c11f3ed1b570b6e8">implyNegatedInequality</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2);</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> </div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ad6dec83ab198a011e429c0f4b3aa218f">integerSplit</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& intVar, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& intPoint);</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span> </div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a929689864e6c95280fcf1caa08ae28e1">trustedRewrite</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2);</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> </div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#af6182f9b295bde40a9047b1651d979a5">rafineStrictInteger</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntConstrThm, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& constr);</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span> </div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a21b67f29c32a44f6194d127feb316d99">simpleIneqInt</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ineq, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS);</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span> </div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a33232797bdaaa27ecd2f077478605bf6">intEqualityRationalConstant</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntConstrThm, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& constr);</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> </div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aacf793e26f8917dbd96d235b9399a18e">cycleConflict</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalitites);</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span> </div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a6a98470138f38710024a7cc8f37706fb">implyEqualities</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalities);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span> </div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#af6d982874e310ba4bdbc796fcbc720fc">implyWeakerInequalityDiffLogic</a>(<span class="keyword">const</span> std::vector<Theorem>& antecedentThms, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& implied);</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span> </div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aee41f9c7c0f2a6b82383076327e316a0">implyNegatedInequalityDiffLogic</a>(<span class="keyword">const</span> std::vector<Theorem>& antecedentThms, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& implied);</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span> </div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#abb0ca6212da8280b0026369e449f900e">expandGrayShadowRewrite</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& theShadow);</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span> </div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ad54e479f1a44912397237a557590c597">compactNonLinearTerm</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& nonLinear);</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span> </div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afe7a4ea7cbce967d7f160c21995c8b39">nonLinearIneqSignSplit</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& ineqThm);</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> </div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8581e89bb73352a8e368e7b87acd78f4">implyDiffLogicBothBounds</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x, std::vector<Theorem>& c1_le_x, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c1,</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  std::vector<Theorem>& x_le_c2, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c2);</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aadb554e4e8877b135fb01d6e2471ccba">powerOfOne</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span> </div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a120563be6dbb828da3e9b6a9d4d35e32">rewriteLeavesConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span> </div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  }; <span class="comment">// end of class ArithTheoremProducerOld</span></div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span> </div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span> } <span class="comment">// end of namespace CVC3</span></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> </div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="preprocessor">#endif</span></div>
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