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<a href="arith__theorem__producer_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*****************************************************************************/</span><span class="comment"></span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">/*!</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * \file arith_theorem_producer.h</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * \brief TRUSTED implementation of arithmetic proof rules</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * Author: Vijay Ganesh, Sergey Berezin</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * Created: Dec 13 02:09:04 GMT 2002</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * and its documentation for any purpose is hereby granted without</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * LICENSE file provided with this distribution.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">/*****************************************************************************/</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#ifndef _cvc3__arith_theorem_producer_h_</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor"></span><span class="preprocessor">#define _cvc3__arith_theorem_producer_h_</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include "<a class="code" href="arith__proof__rules_8h.html" title="Arithmetic proof rules.">arith_proof_rules.h</a>"</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include "<a class="code" href="theorem__producer_8h.html">theorem_producer.h</a>"</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include "<a class="code" href="theory__arith__new_8h.html">theory_arith_new.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>TheoryArithNew;</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_1ArithTheoremProducer.html"> 32</a></span>  <span class="keyword">class </span><a class="code" href="classCVC3_1_1ArithTheoremProducer.html">ArithTheoremProducer</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_1ArithTheoremProducer.html#ad2c70acba668e2582f0ebd9533646338"> 33</a></span>  <a class="code" href="classCVC3_1_1TheoryArithNew.html">TheoryArithNew</a>* <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad2c70acba668e2582f0ebd9533646338">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_1ArithTheoremProducer.html#a3cb8580c7627250ffe999de9a1b2c8c3" 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_1ArithTheoremProducer.html#a47a517c15b57ba19b7759a4ba925e306" 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_1ArithTheoremProducer.html#ab20380e74e431d9956c588d45d5121a4" 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_1ArithTheoremProducer.html#a77e9c5681a02ab61f1311628e843d3db" 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_1ArithTheoremProducer.html#a10c569edc893a67b42af659633b3f20d" 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_1ArithTheoremProducer.html#a69adf7d70a6a71e5c0e3489535a18108" 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_1ArithTheoremProducer.html#a32e61136df79a76fe1ed853ee6b8dc2e" 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_1ArithTheoremProducer.html#a41da83b4624daa43a84bc049b5b7d836" 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_1ArithTheoremProducer.html#ad727620082aea32b487863ac5888eb1b" 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_1ArithTheoremProducer.html#a073ec1476668043be44ae96519eae36d" title="Compute the special modulus: i - m*floor(i/m+1/2)">substitute</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& term, <a class="code" href="classCVC3_1_1ExprMap.html">ExprMap<Expr></a>& eMap);</div>
<div class="line"><a name="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="comment"> /*@}*/</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">public</span>:<span class="comment"></span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment"> //! Constructor</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a8216db52c44de1ba9a50ca6dfea24720"> 67</a></span> <span class="comment"></span> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a8216db52c44de1ba9a50ca6dfea24720" title="Constructor.">ArithTheoremProducer</a>(<a class="code" href="classCVC3_1_1TheoremManager.html">TheoremManager</a>* tm, <a class="code" href="classCVC3_1_1TheoryArithNew.html">TheoryArithNew</a>* theoryArith):</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <a class="code" href="classCVC3_1_1TheoremProducer.html">TheoremProducer</a>(tm), <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad2c70acba668e2582f0ebd9533646338">d_theoryArith</a>(theoryArith) { }</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"></span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"> //! Create Expr from Rational (for convenience)</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ae0d46b17ef012eabbbe62cac026bfab9"> 71</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_1ArithTheoremProducer.html#ae0d46b17ef012eabbbe62cac026bfab9" 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="l00072"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a4606a94098ae94cdae1b924dc7f7b4ae"> 72</a></span>  <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a4606a94098ae94cdae1b924dc7f7b4ae">realType</a>() { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad2c70acba668e2582f0ebd9533646338">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#a03fa81194322b92c488033695bec7204">realType</a>(); }</div>
<div class="line"><a name="l00073"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a8b33391347e9741339b674abd5c4fbf2"> 73</a></span>  <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a8b33391347e9741339b674abd5c4fbf2">intType</a>() { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad2c70acba668e2582f0ebd9533646338">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#ad3e47bba6c50745ad194cf273aa1d146">intType</a>(); }<span class="comment"></span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"> //! Construct the dark shadow expression representing lhs <= rhs</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a9dfab0a471e7a705264be04007ac61e5"> 75</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_1ArithTheoremProducer.html#a9dfab0a471e7a705264be04007ac61e5" 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="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad2c70acba668e2582f0ebd9533646338">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="l00077"></a><span class="lineno"> 77</span>  }<span class="comment"></span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"> //! Construct the gray shadow expression representing c1 <= v - e <= c2</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</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="l00080"></a><span class="lineno"> 80</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a1684298bef4bf1efdccb7078f5a6c96f"> 81</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_1ArithTheoremProducer.html#a1684298bef4bf1efdccb7078f5a6c96f" 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="l00082"></a><span class="lineno"> 82</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="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad2c70acba668e2582f0ebd9533646338">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="l00084"></a><span class="lineno"> 84</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></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"></span> <span class="comment">// Canonization rules</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"></span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="comment">// ==> x = 1 * x</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a7568925b6c26f1c7ba882893f596d214" 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="l00092"></a><span class="lineno"> 92</span> </div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="comment">// ==> -(e) = (-1) * e</span></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aaafdbe9dcc49728cc2bf16b43045c193" 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="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="comment">// ==> x - y = x + (-1) * y</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ab369e518fc2ee411503253fa0b1515d6" 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="l00098"></a><span class="lineno"> 98</span> </div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="comment">// Rule for unary minus: it just converts it to division by -1,</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a4671174ae8ff61c52f16ddd53a3cdd27" 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="l00101"></a><span class="lineno"> 101</span> </div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="comment">// Rules for division by constant 'd'</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">// (c) / d ==> (c/d), takes c and d</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a515e5d076ed135a6d943c2f5d5e34188" 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="l00105"></a><span class="lineno"> 105</span>  <span class="comment">// (c * x) / d ==> (c/d) * x, takes (c*x) and d</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a4d2d8da9de6d6faaa07758c01e3a9fe8" 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="l00107"></a><span class="lineno"> 107</span>  <span class="comment">// (+ c ...)/d ==> push division to all the coefficients.</span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// The result is not canonical, but canonizing the summands will</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="comment">// make it canonical.</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="comment">// Takes (+ c ...) and d</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a4338b85f1dd0fca0cc58e6b7259a20b4" 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="l00112"></a><span class="lineno"> 112</span>  <span class="comment">// x / d ==> (1/d) * x, takes x and d</span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aa651eb7a4d20a77135efa2d3e984c355" 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="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="comment">// Canon Rules for multiplication</span></div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> </div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">// TODO Deepak:</span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</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="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// 1) Rational constant</span></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// 2) Arithmetic Leaf (var or term from another theory)</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="comment">// 3) (POW rational leaf)</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</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="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// 5) (PLUS rational sterm_1 sterm_2 ...) where each sterm is of </span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="comment">// type (2) or (3) or (4) </span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keyword">static</span> <span class="keywordtype">bool</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a23faa6b30e4b01d7540ac1e22e6e06ce">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="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_1ArithTheoremProducer.html#af24b2bc3bc03bc320707362f2460dd0e">simplifiedMultExpr</a>(std::vector<Expr> & mulKids);</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_1ArithTheoremProducer.html#a10ebfab26aa4ee1a147f08d8f6b94c45">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="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_1ArithTheoremProducer.html#a48b21552a97a3a75ae469fb48c155e51">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="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_1ArithTheoremProducer.html#aebf0a0b539104e2190b53351efc6116b">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="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_1ArithTheoremProducer.html#aabc24cdaf5d3a390f9880937bac17311">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="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_1ArithTheoremProducer.html#aae1bc41d54f8b148ce5cf9425ac688af">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="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_1ArithTheoremProducer.html#a05b2608fd280890cb49bf4534a54e304">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="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> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a9548361051bb6febc314faa107d2c2f5">canonCombineLikeTerms</a>(<span class="keyword">const</span> std::vector<Expr> & sumExprs);</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</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="l00136"></a><span class="lineno"> 136</span>  <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a0b344f367f01d240d997df7edfe1a12c">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="l00137"></a><span class="lineno"> 137</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_1ArithTheoremProducer.html#ac0363ff2f51ad1173ed1e46046b0654a">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="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_1ArithTheoremProducer.html#ab5166b206f49897a6a49ba0014c0b808">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="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_1ArithTheoremProducer.html#a41f7000c783a82e9a86cad823b06bff4" 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="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_1ArithTheoremProducer.html#a7b07ab799dbdf80254df3ec7fc35d36d">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="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_1ArithTheoremProducer.html#afb0c2a89f3373dcb26cd516714d0e49a">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="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_1ArithTheoremProducer.html#a6a829cb16f960f9e7c2f25ea4906eaba">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="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_1ArithTheoremProducer.html#a70a381c22184655fb6d4f3b621bf216b">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="l00144"></a><span class="lineno"> 144</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a7c7c860b193ec63a776dd13613aeca25" 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="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"> /**</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</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="l00148"></a><span class="lineno"> 148</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="l00149"></a><span class="lineno"> 149</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment"> * @param e the expression to transform </span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"> * @return rewrite theorem representing the transformation </span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a77b99e94956d407e5cd20701e6771120">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="l00154"></a><span class="lineno"> 154</span> <span class="comment"></span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"> /** e[0]/e[1] ==> e[0]*(e[1])^-1 */</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a92540cc58f6203c2904fc2bd197190da">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="l00157"></a><span class="lineno"> 157</span>  <span class="comment"></span></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</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="l00159"></a><span class="lineno"> 159</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a9bd77385dd0cbaac271aaab4b6c6ec09">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="l00160"></a><span class="lineno"> 160</span> </div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="comment">// t*c ==> c*t, takes constant c and term t</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af6ba91fa47c4c9139c4d93fe3de0112f" 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="l00163"></a><span class="lineno"> 163</span>  <span class="comment">// t1*t2 ==> Error, takes t1 and t2 where both are non-constants</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a529fe89fea243d932879a1a74e9d36a7" 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="l00165"></a><span class="lineno"> 165</span>  <span class="comment">// 0*t ==> 0, takes 0*t</span></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a55ec89d6cf310694e9f4b1013a795ce2" 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="l00167"></a><span class="lineno"> 167</span>  <span class="comment">// 1*t ==> t, takes 1*t</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ae5a6e1b2c7b9239b7e53027c51a2dc7e" 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="l00169"></a><span class="lineno"> 169</span>  <span class="comment">// c1*c2 ==> c', takes constant c1*c2 </span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#affbdf02016310d8cd6a9037fdd9eddc6" 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="l00171"></a><span class="lineno"> 171</span>  <span class="comment">// c1*(c2*t) ==> c'*t, takes c1 and c2 and t</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> </div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad51f0d5c3232b6c247939a10e253f53d" 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="l00174"></a><span class="lineno"> 174</span>  <span class="comment">// c1*(+ c2 v1 ...) ==> (+ c' c1v1 ...), takes c1 and the sum</span></div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ab0e0e14c71501a9f8208963c54010fe4" 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="l00176"></a><span class="lineno"> 176</span>  <span class="comment">// c^n = c' (compute the constant power expression)</span></div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af673275ae1c3dc606b29979b60df35c5" 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="l00178"></a><span class="lineno"> 178</span> </div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="comment">// Rules for addition</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="comment">// flattens the input. accepts a PLUS expr</span></div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a19964269c705bafbe69cb1052fe7bec8" 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="l00182"></a><span class="lineno"> 182</span>  </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="comment">// Rules for addition</span></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="comment">// combine like terms. accepts a flattened PLUS expr</span></div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ac9ee451992ab00f200ee8aee26e99e0c" 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="l00186"></a><span class="lineno"> 186</span>  </div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="comment">// 0 = (* e1 e2 ...) <=> 0 = e1 OR 0 = e2 OR ...</span></div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a0040d5d848f7040df940b92d95a75930">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="l00189"></a><span class="lineno"> 189</span> </div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="comment">// 0 = (^ c x) <=> false if c <=0</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="comment">// <=> 0 = x if c > 0</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a9cd618abf322c0389f1fc40f274059c2">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="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="comment">// x^n = y^n <=> x = y (if n is odd)</span></div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="comment">// x^n = y^n <=> x = y OR x = -y (if n is even)</span></div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3c454b863142345e1093663fbb89d306">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="l00197"></a><span class="lineno"> 197</span> </div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="comment">// x^n = c <=> x = root (if n is odd and root^n = c)</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</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="l00200"></a><span class="lineno"> 200</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a21456f49d3a6711f21e3c13fb3c0d34a">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="l00201"></a><span class="lineno"> 201</span> </div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="comment">// x^n = c <=> false (if n is even and c is negative)</span></div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#afbf059903de8b1e87aef9a4a75340d6c">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="l00204"></a><span class="lineno"> 204</span> </div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</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="l00206"></a><span class="lineno"> 206</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aa3838fe1c003a9f47f3ec8344d192dea">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="l00207"></a><span class="lineno"> 207</span> </div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="comment">// e[0] kind e[1] <==> true when e[0] kind e[1],</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="comment">// false when e[0] !kind e[1], for constants only</span></div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a621015d4894231ecd9ab465494e9c9c8" 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="l00211"></a><span class="lineno"> 211</span> </div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="comment">// e[0] kind e[1] <==> 0 kind e[1] - e[0]</span></div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3eb1309c184247837239c098d9c9100a" 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="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="comment">// e[0] kind e[1] <==> e[0] - e[1] kind 0</span></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a8196042ba713a7c782ee4b5eb4c69ccc" 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="l00217"></a><span class="lineno"> 217</span> </div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="comment">// x kind y <==> x + z kind y + z</span></div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3c3041eb3b0144e21d72ffe6999953e2" 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="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>& y, </div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</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="l00222"></a><span class="lineno"> 222</span> </div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="comment">// x = y <==> x * z = y * z</span></div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ae66ddbc1457e3c032ea9059625059992" 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="l00225"></a><span class="lineno"> 225</span> </div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="comment">// x = y <==> z=0 OR x * 1/z = y * 1/z</span></div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aa371616db9ac1a4a9c7a4b1ce0f2a05c">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="l00228"></a><span class="lineno"> 228</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[0]*z LT|LE|GT|GE e[1]*z</span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</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="l00231"></a><span class="lineno"> 231</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3d245f36a2e42684ec2fd9356d89111f" 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="l00232"></a><span class="lineno"> 232</span> </div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="comment">// x = y ==> x <= y and x >= y</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a517d45514aefcab0dc6aabb400f149fd" 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="l00235"></a><span class="lineno"> 235</span> </div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="comment">// "op1 GE|GT op2" <==> op2 LE|LT op1</span></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af069fc1b320c0455ec7cde192668884b" 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="l00238"></a><span class="lineno"> 238</span>  </div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">// NOT (op1 LT op2) <==> (op1 GE op2)</span></div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="comment">// NOT (op1 LE op2) <==> (op1 GT op2)</span></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="comment">// NOT (op1 GT op2) <==> (op1 LE op2)</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="comment">// NOT (op1 GE op2) <==> (op1 LT op2)</span></div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a07368f8a2e12b5c189645a99bc934102" 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="l00244"></a><span class="lineno"> 244</span> </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_1ArithTheoremProducer.html#a8092c96a87d952fc1e572bb9237ff994" 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="l00246"></a><span class="lineno"> 246</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a6e14251c516153e14539a34598daca04" 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="l00247"></a><span class="lineno"> 247</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a7f4c82e18e7a3ed3b5b22a6ce7d7cf27" 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="l00248"></a><span class="lineno"> 248</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="l00249"></a><span class="lineno"> 249</span>  </div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aef6fd1261bea182d4554d0423803b05e" 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="l00251"></a><span class="lineno"> 251</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& axLEalpha,</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>& isIntAlpha,</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>& isIntBeta,</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</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="l00255"></a><span class="lineno"> 255</span>  </div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aaf64935bb620ab79fd7383f1913bd8b8" 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="l00257"></a><span class="lineno"> 257</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& axLEalpha,</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>& isIntAlpha,</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>& isIntBeta,</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</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="l00261"></a><span class="lineno"> 261</span>  </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_1ArithTheoremProducer.html#aafadfc6ae6013ab18a7b4ee570cce16a">expandDarkShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a9dfab0a471e7a705264be04007ac61e5" title="Construct the dark shadow expression representing lhs <= rhs.">darkShadow</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_1ArithTheoremProducer.html#ac8a2c0a97ace8f17153ad784c87ba5a2" 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_1ArithTheoremProducer.html#a1684298bef4bf1efdccb7078f5a6c96f" 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_1ArithTheoremProducer.html#a14af8b5ecbfaaee4600453bd9d681838" 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_1ArithTheoremProducer.html#a1684298bef4bf1efdccb7078f5a6c96f" 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_1ArithTheoremProducer.html#acaa835c8569f6667fa26bfedb0502cf1">splitGrayShadowSmall</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a1684298bef4bf1efdccb7078f5a6c96f" 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_1ArithTheoremProducer.html#ac6714d4922aea3413f9aeed742bc645e" 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_1ArithTheoremProducer.html#a1684298bef4bf1efdccb7078f5a6c96f" 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_1ArithTheoremProducer.html#af091e13254c983370c46707a03b1ad30" 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_1ArithTheoremProducer.html#a1684298bef4bf1efdccb7078f5a6c96f" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af0070c5da95d33029e54b1d669d5b1f0" 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="l00269"></a><span class="lineno"> 269</span> <span class="comment"></span></div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="comment"> //! Implements j(c,b,a)</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment"></span><span class="comment"> /*! accepts 3 integers a,b,c and returns</span></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment"> * (b > 0)? (c+b) mod a : (a - (c+b)) mod a</span></div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a529e92e59e9009e3330a8592c9cb56fe" 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="l00275"></a><span class="lineno"> 275</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& b,</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& a);</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span> </div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ac5d4056f00cee80d73b5b46f63bd5b3d">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="l00279"></a><span class="lineno"> 279</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="l00280"></a><span class="lineno"> 280</span>  </div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af55c5d0a2626f955b0843381ca8b50f3">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="l00282"></a><span class="lineno"> 282</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="l00283"></a><span class="lineno"> 283</span>  </div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a92936e3de514c430659486b00e84b0a9">intVarEqnConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& eqn, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>);</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span> </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_1ArithTheoremProducer.html#a85e9c7d93d6d1433fea606b0c3878e25">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="l00287"></a><span class="lineno"> 287</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a49d6559f50d51cde3c2e723c2a254cff" title="Equality elimination rule for integers: See the detailed description for explanations.">eqElimIntRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& eqn, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>,</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keyword">const</span> std::vector<Theorem>& isIntVars);</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span> </div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af1baf70d6108dc52cbb9704e2a8889ec" title="return e <=> TRUE/FALSE for e == IS_INTEGER(c), where c is a constant">isIntConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> </div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a512f22a4a025477ced8c27f3d62809d7">equalLeaves1</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a77ae567431bf98e20cc08903deb2ec99">equalLeaves2</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a8de6b6b44c60cf495b455b980a7c681b">equalLeaves3</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a97768870957319cdc68eb94694a37dc5">equalLeaves4</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> </div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3d6e1d8668360c20b5a6a47e3fcc4612" title="x /= y ==> (x < y) OR (x > y)">diseqToIneq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& diseq);</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  </div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a753c339b31e38915ae6f06e0fe6e48da">dummyTheorem</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  </div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a23051d23d509f9cda35c64d4a5ff1dbf">oneElimination</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x);</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  </div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad4513630a9eec6c841b527222a79ea1d">clashingBounds</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& lowerBound, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& upperBound);</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  </div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3b2bea72cd9163daa7c41388037bca29">addInequalities</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm2);</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3b2bea72cd9163daa7c41388037bca29">addInequalities</a>(<span class="keyword">const</span> std::vector<Theorem>& thms);</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  </div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a364ef37224bae3afb4f62a5c0f75d02c">implyWeakerInequality</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2);</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  </div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a1bf4d45330b587882e726daa9117cdfb">implyNegatedInequality</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2);</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> </div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ab9395a2ee958d70c780df2514e517320">integerSplit</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& intVar, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& intPoint);</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  </div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a43fa5f7c8c3ad3915de7f068ac8cefbd">trustedRewrite</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2);</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  </div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a4b28aa17702ca3f9703e61ca012ca236">rafineStrictInteger</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntConstrThm, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& constr);</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  </div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#afd5bca9b136254b904b931680180ac83">simpleIneqInt</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ineq, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS);</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  </div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad5f121b6b7d6b8ae951dfb4cce064575">intEqualityRationalConstant</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntConstrThm, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& constr);</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  </div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a0111aa5645658dbd6a4bc030178edb94">cycleConflict</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalitites);</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  </div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#abb8aff055ea56ad8de2b66fd9a7aeba9">implyEqualities</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalities);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  </div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ae3a7aa0ebe8e84b806efaa59278ea75e">implyWeakerInequalityDiffLogic</a>(<span class="keyword">const</span> std::vector<Theorem>& antecedentThms, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& implied);</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  </div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ab794c1f9d6e971ac56e0063f409b4774">implyNegatedInequalityDiffLogic</a>(<span class="keyword">const</span> std::vector<Theorem>& antecedentThms, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& implied);</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  </div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a84a9652acc5908e5d1ead5c54c1f2d90">expandGrayShadowRewrite</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& theShadow);</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  </div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ae43400e7e4c9e3695a75da3bd5718eda">compactNonLinearTerm</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& nonLinear);</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  </div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a9edd8b9ee6a8b4d14e9a2f967b78d52f">nonLinearIneqSignSplit</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& ineqThm);</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  </div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a45d8f89bdb0e57ddbaec273a24bf34b4">implyDiffLogicBothBounds</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x, std::vector<Theorem>& c1_le_x, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c1, </div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  std::vector<Theorem>& x_le_c2, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c2);</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a0433b1ba53a33275015c26450acb09d0">powerOfOne</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e);</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span> </div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  }; <span class="comment">// end of class ArithTheoremProducer</span></div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span> </div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span> } <span class="comment">// end of namespace CVC3</span></div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span> </div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="preprocessor">#endif</span></div>
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