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<a href="arith__theorem__producer3_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_producer3.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_producer3_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_producer3_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__arith3_8h.html">theory_arith3.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>  <span class="keyword">class </span>TheoryArith3;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  </div>
<div class="line"><a name="l00032"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html"> 32</a></span>  <span class="keyword">class </span><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html">ArithTheoremProducer3</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="l00033"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07"> 33</a></span>  <a class="code" href="classCVC3_1_1TheoryArith3.html">TheoryArith3</a>* <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">d_theoryArith</a>;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keyword">private</span>:<span class="comment"></span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> /*! \name Auxiliary functions for eqElimIntRule()</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"> * Methods that compute the subterms used in eqElimIntRule()</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> *@{</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> */</span><span class="comment"></span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> //! Compute the special modulus: i - m*floor(i/m+1/2)</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"></span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ada3b48ce9720177b4a427237efe0453f" 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="l00041"></a><span class="lineno"> 41</span> <span class="comment"> //! Create the term 't'. See eqElimIntRule().</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</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_1ArithTheoremProducer3.html#ab70323686fd8775952a2709a6c8c754b" 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="l00043"></a><span class="lineno"> 43</span> <span class="comment"> //! Create the term 't2'. See eqElimIntRule().</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</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_1ArithTheoremProducer3.html#adf974179ea62c2196a87fb9c2199f6cd" 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="l00045"></a><span class="lineno"> 45</span> <span class="comment"> //! Create the term 't3'. See eqElimIntRule().</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</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_1ArithTheoremProducer3.html#a6bad08f3833720448803251dfa234e36" 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="l00047"></a><span class="lineno"> 47</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="l00048"></a><span class="lineno"> 48</span> <span class="comment"> * vector of similar monomials (in 'summands') with coefficients</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"> * mod(a_i, m). If divide flag is true, the coefficients will be</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment"> * mod(a_i,m)/m.</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aa21c4aa75f54e05bdc772b0e2d37b669" 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="l00053"></a><span class="lineno"> 53</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="l00054"></a><span class="lineno"> 54</span>  <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a5245a34c6f9e903db87e17df1d33c09d" 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="l00055"></a><span class="lineno"> 55</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="l00056"></a><span class="lineno"> 56</span>  <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a36838065b24c16503ef6cf8164de44a8" 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="l00057"></a><span class="lineno"> 57</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="l00058"></a><span class="lineno"> 58</span>  <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aea07da55e987ccd27d0f57e08558af01" 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="l00059"></a><span class="lineno"> 59</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="l00060"></a><span class="lineno"> 60</span> <span class="comment"> //! Compute floor(i/m+1/2) + mod(i,m)</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"></span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a077f8d0dab986b01d390668f6af1afa2" 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="l00062"></a><span class="lineno"> 62</span>  <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a3d0129d121975b0141d77ba6f458c182" 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);<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_1ArithTheoremProducer3.html#a56fb5871062ffe12510c4cd4ba65b745"> 66</a></span> <span class="comment"></span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a56fb5871062ffe12510c4cd4ba65b745" title="Constructor.">ArithTheoremProducer3</a>(<a class="code" href="classCVC3_1_1TheoremManager.html">TheoremManager</a>* tm, <a class="code" href="classCVC3_1_1TheoryArith3.html">TheoryArith3</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_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">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_1ArithTheoremProducer3.html#a4440979f29e7ec3519212ff1e23d758f"> 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_1ArithTheoremProducer3.html#a4440979f29e7ec3519212ff1e23d758f" 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_1ArithTheoremProducer3.html#ad010c33575ebd1dc229c2a1526c229c5"> 71</a></span>  <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad010c33575ebd1dc229c2a1526c229c5">realType</a>() { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">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_1ArithTheoremProducer3.html#a04f5df44759216fd1182bd745cfc6a82"> 72</a></span>  <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a04f5df44759216fd1182bd745cfc6a82">intType</a>() { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">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_1ArithTheoremProducer3.html#afe495b6c58dd0c89c84b64c5194eeeaa"> 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_1ArithTheoremProducer3.html#afe495b6c58dd0c89c84b64c5194eeeaa" 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_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">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_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8"> 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_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" 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_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">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_1ArithTheoremProducer3.html#a23340f90880cb869fdcfe6e69a7a2631" 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_1ArithTheoremProducer3.html#a878e091ad5cfd2877ddce73d6f664e16" 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_1ArithTheoremProducer3.html#ab0d610d377cc20e3ce16823713d25403" 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_1ArithTheoremProducer3.html#a9bf439248afb24bb63ea435193b68524" 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_1ArithTheoremProducer3.html#a3a2bf5e3b8c71543b1512f1606825a02" 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_1ArithTheoremProducer3.html#a39a2efadcc13383fd860340c6d76db54" 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_1ArithTheoremProducer3.html#a897c950b6bb741189f1c33752159b587" 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_1ArithTheoremProducer3.html#a9fddb49ed54796e6a5487be554eb14f4" 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_1ArithTheoremProducer3.html#a1923e590a205cefe9ef50d336e99c9e5">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_1ArithTheoremProducer3.html#aea589889127864f327d4d71800f096b7">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_1ArithTheoremProducer3.html#ad49508debdf58df9d8333cd140c850a3">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_1ArithTheoremProducer3.html#a747b71c44a0bad76328039a2fc123363">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_1ArithTheoremProducer3.html#ae709408bffa6ff2016619a05febe63f5">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_1ArithTheoremProducer3.html#a1765748e34d12d99b3bdf57f3ba49d49">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_1ArithTheoremProducer3.html#ad9ff33794685a95c453d41bf1fd9d0aa">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_1ArithTheoremProducer3.html#a9bf1d7c7d567deab2e5decc8c4e82fdc">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_1ArithTheoremProducer3.html#af61545eb36910fba4fa1b69e6febb354">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_1ArithTheoremProducer3.html#ad5dec14920bc52be7b9fdfb458ba2e1b">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_1ArithTheoremProducer3.html#ab327e6f313e952c0380fe7460bd7d36c">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_1ArithTheoremProducer3.html#aa1ab000ca8a6a2605b2cb57f8b881d91">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_1ArithTheoremProducer3.html#acbd2c2b8d5a0728aa00dcf55c7c646f2" 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_1ArithTheoremProducer3.html#addd3884d42a6e4637e9bda79d4af6574">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_1ArithTheoremProducer3.html#a84b1ec96629fa2ae52792a582ba7a63a">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_1ArithTheoremProducer3.html#a02b89064723281b69105ce11ecaf80c7">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_1ArithTheoremProducer3.html#a94090722e5ab797e97cdb14458c40742">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_1ArithTheoremProducer3.html#a1a4b78b01763b1ca5a80c0211bc3ba4b" 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_1ArithTheoremProducer3.html#aad289f36b55fe8be7f7af0f62aedaae8">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_1ArithTheoremProducer3.html#acfe4060947cb28e9fc9c4ea859df565c">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_1ArithTheoremProducer3.html#a627a219305f83b200e36b28b1865729a">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_1ArithTheoremProducer3.html#a401fca0c453a94c8c0053eb77e014af0" 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_1ArithTheoremProducer3.html#a294916be1e9ac30e3c824b0b8e4ff093" 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_1ArithTheoremProducer3.html#a55fb07d5df2b4068bf5df327ae0d89d4" 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_1ArithTheoremProducer3.html#aed0a2d1337910f3027ac867e0f18b8de" 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_1ArithTheoremProducer3.html#a4ea3884dff8c1606fd05e61eb78e379d" 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_1ArithTheoremProducer3.html#a9e5b7c75f1f662071942150df1a4d69e" 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_1ArithTheoremProducer3.html#a2765c1485aac81cc42ed3186f7a1f244" 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_1ArithTheoremProducer3.html#a5347a8208d4d7aa05fad463bd6da8c41" 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_1ArithTheoremProducer3.html#a5ec4889e730c0b1d4fb584d16af08a9d" 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_1ArithTheoremProducer3.html#a245f64776d0b1fbd14d18bb145f717e4" 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_1ArithTheoremProducer3.html#a57eafe7c2a127ca4b4706437b777d610">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_1ArithTheoremProducer3.html#acbea7826fe54b91e8d4bc2c21f7137ae">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_1ArithTheoremProducer3.html#ab29b63e40b7f2c624e6e4f11c4eff27e">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_1ArithTheoremProducer3.html#a942f9f0fc0ceff798b607e9fe032175a">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_1ArithTheoremProducer3.html#abe913a6cc9430faf8f0ac50ec51aa36c">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_1ArithTheoremProducer3.html#a946832931094bb746277d8b95c471690">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_1ArithTheoremProducer3.html#a7a2a8059fa49da5a8877b28b1cfa445a" 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_1ArithTheoremProducer3.html#aca76a2dbee73d7ad9e2529ac8ce142a4" 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_1ArithTheoremProducer3.html#aedad2be1c60515921f8c3761581afca5" 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_1ArithTheoremProducer3.html#ab190e4d8fefb74f2a8117ca17ae49b48" 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_1ArithTheoremProducer3.html#afd7a6da45999fb3237cdbbbf9c5f19e8" 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_1ArithTheoremProducer3.html#a7bf31f4d4bd6e3f7ff7e37dd5236a792">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_1ArithTheoremProducer3.html#a8af6455fe4a8889cfb7b0b8c865b847c" 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_1ArithTheoremProducer3.html#ad2f144d3a2ffe108e0d8e7df8e263832" 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_1ArithTheoremProducer3.html#a216a950228aad3cdef0c5dd5213be4fb" 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_1ArithTheoremProducer3.html#a27bb939c33616b21a83aabdb5d47a660" 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_1ArithTheoremProducer3.html#a6f08ce700f85f9ba2967ecee42e7a550" 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_1ArithTheoremProducer3.html#a955e74558aee9ebc9de4c084819e93ac" 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_1ArithTheoremProducer3.html#aaba7798eb77a93ac0de8978507dca731" 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_1ArithTheoremProducer3.html#a2ad479414c401fb8a4ea9631cbdd95c0" 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_1ArithTheoremProducer3.html#a8b2e8589d24fc69616ba431588c50b3e" 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_1ArithTheoremProducer3.html#a372efa694fb08c901deff55f5f108ffb">expandDarkShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#afe495b6c58dd0c89c84b64c5194eeeaa" 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_1ArithTheoremProducer3.html#aacc831490c52da277133fe625522216f" 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_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" 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_1ArithTheoremProducer3.html#ae609e58a7bee454d0f18dc1465cd2167" 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_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" 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_1ArithTheoremProducer3.html#aab0ccd490624628fa990b1dd473e7e8a">splitGrayShadowSmall</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" 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_1ArithTheoremProducer3.html#ab9dd38464b6e02af6d7c570119c6aec3" 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_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" 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_1ArithTheoremProducer3.html#a43d1cf15faefe439c344508bf60e5e96" 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_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" 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_1ArithTheoremProducer3.html#a0a5eb9028805dd1ee141713b7c70be77" 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_1ArithTheoremProducer3.html#afa3e14a6cb004a107d915df0088ed16c" 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_1ArithTheoremProducer3.html#a91447c7423622c037a2956114fd549f4">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_1ArithTheoremProducer3.html#a55c056040dc960b598706a94650acccb">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>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a608b3a7da8f2824d3cc8188d7606396e">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="l00284"></a><span class="lineno"> 284</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad2438a34ff1edb7268495d4105cb6c9c">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="l00285"></a><span class="lineno"> 285</span> </div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a1f5430f425efc533ca5881aaaeb42554" 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="l00287"></a><span class="lineno"> 287</span>  <span class="keyword">const</span> std::vector<Theorem>& isIntVars);</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span> </div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a24216d1be10b57272b918ba416783b76" 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="l00290"></a><span class="lineno"> 290</span> </div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#acb64cdcb59f042dd38a9bf9b70f043ad">equalLeaves1</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);</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_1ArithTheoremProducer3.html#ae97e571a8d541a31aef5c1c703190437">equalLeaves2</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_1ArithTheoremProducer3.html#aba1a7d51f8b8291c30cc32c0f3ff5a4d">equalLeaves3</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_1ArithTheoremProducer3.html#a5876760c9171eca18490c779cc2bbc73">equalLeaves4</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> </div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a20fdbcbe80fa06a175aae548af7d2519" 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="l00297"></a><span class="lineno"> 297</span>  </div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ae1e994559a2318ec45a758042371a71d">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="l00299"></a><span class="lineno"> 299</span>  </div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a2caebbed8d00af9c80195413ed2cc568">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="l00301"></a><span class="lineno"> 301</span>  </div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#af05299dbe2defe9679365201cd60c516">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="l00303"></a><span class="lineno"> 303</span>  </div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a301d62f207b9cfd50096417d1f5852df">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="l00305"></a><span class="lineno"> 305</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a301d62f207b9cfd50096417d1f5852df">addInequalities</a>(<span class="keyword">const</span> std::vector<Theorem>& thms);</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  </div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ae856ca9fab9699b655d7fd76cdf778d4">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="l00308"></a><span class="lineno"> 308</span>  </div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a1797b422d1100edc2464666121d7017b">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="l00310"></a><span class="lineno"> 310</span> </div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ae25218af53e642382f30948adc991313">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="l00312"></a><span class="lineno"> 312</span>  </div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad58ee7b299de278620860c9d67a2662b">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="l00314"></a><span class="lineno"> 314</span>  </div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a7638b18d73c05e7bedad7c4cdfeca809">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="l00316"></a><span class="lineno"> 316</span> </div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a6fe0e5ebaf81278f55759fff05c275c1">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="l00318"></a><span class="lineno"> 318</span>  </div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a84ec7197bec26c33753e98b6adf55dce">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="l00320"></a><span class="lineno"> 320</span>  </div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a5411413ef39cb6029a8e85fc03908de3">cycleConflict</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalitites);</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  </div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a1efa679a45d71f60bf2be6f4f7a4430d">implyEqualities</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalities);</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  </div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a8e90a0d0e2050a7f0eb1dde6df7f6842">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="l00326"></a><span class="lineno"> 326</span>  </div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a6ef98983cca8d3723f50fbea60c37cef">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="l00328"></a><span class="lineno"> 328</span>  </div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aa9b6fa1339b7e68cb730bdf2f63c0914">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="l00330"></a><span class="lineno"> 330</span>  </div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aac90a712f81d969d8aa0322b4d31de0b">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="l00332"></a><span class="lineno"> 332</span>  </div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aaa91789edbf7fb936789379dd15a3a4f">nonLinearIneqSignSplit</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& ineqThm);</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  </div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a9edd45196fbd8e61a4927134fde15e97">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="l00336"></a><span class="lineno"> 336</span>  std::vector<Theorem>& x_le_c2, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c2);</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  </div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#abf49b0eeb6087702dd1a8e9c03f7379a">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="l00339"></a><span class="lineno"> 339</span> </div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  }; <span class="comment">// end of class ArithTheoremProducer3</span></div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span> </div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span> } <span class="comment">// end of namespace CVC3</span></div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span> </div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span> <span class="preprocessor">#endif</span></div>
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