<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">A</font> be   <a href="funct_8.html#V1" title="FUNCT_8:attr.1">symmetrical</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">G</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Olive" title="b1">F</font> <a href="funct_8.html#R1" title="FUNCT_8:pred.1">is_even_on</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Olive" title="b2">G</font> <a href="funct_8.html#R1" title="FUNCT_8:pred.1">is_even_on</a> <font color="Maroon" title="c1">A</font> holds <br/><font color="Olive" title="b1">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b2">G</font> <a href="funct_8.html#R1" title="FUNCT_8:pred.1">is_even_on</a> <font color="Maroon" title="c1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">G</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> <a href="funct_8.html#R1" title="FUNCT_8:pred.1">is_even_on</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c3">G</font> <a href="funct_8.html#R1" title="FUNCT_8:pred.1">is_even_on</a> <font color="Maroon" title="c1">A</font> implies <font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font> <a href="funct_8.html#R1" title="FUNCT_8:pred.1">is_even_on</a> <font color="Maroon" title="c1">A</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:37"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="funct_8.html#R1" title="FUNCT_8:pred.1">is_even_on</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">and </span><br/><a NAME="E2:37"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<font color="Maroon" title="c3">G</font> <a href="funct_8.html#R1" title="FUNCT_8:pred.1">is_even_on</a> <font color="Maroon" title="c1">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font> <a href="funct_8.html#R1" title="FUNCT_8:pred.1">is_even_on</a> <font color="Maroon" title="c1">A</font></span><br/>

<a NAME="E3:37"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="funct_8.html#D5" target="_self" title="FUNCT_8:def.5">Def5</a></span>;<br/>
<a NAME="E4:37"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
<font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font> is  <a href="funct_8.html#V4" title="FUNCT_8:attr.4">even</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="funct_8.html#D5" target="_self" title="FUNCT_8:def.5">Def5</a></span>;<br/>
<a NAME="E5:37"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
<font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="funct_8.html#D5" target="_self" title="FUNCT_8:def.5">Def5</a></span>;<br/>
<a NAME="E6:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A6</font></span>: 
<font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></span>;<br/>
<a NAME="E7:37"/><span class="lab"><font color="Green" title="E23">A7</font></span>: 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>;<br/>
<a NAME="E8:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A8</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></span>;<br/>
<a NAME="E9:37"/><span class="lab"><font color="Green" title="E25">A9</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font> is  <a href="funct_8.html#V4" title="FUNCT_8:attr.4">even</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="funct_8.html#D5" target="_self" title="FUNCT_8:def.5">Def5</a></span>;<br/>
<a NAME="E10:37"/>
for <font color="Olive" title="b1">x</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> &amp;  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> &amp;  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:37_1"/><span class="lab"><font color="Green" title="E26">A10</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:37_1"/><span class="lab"><font color="Green" title="E27">A11</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span><br/>

<a NAME="E3:37_1"/><span class="lab"><font color="Green" title="E28">A12</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></span>;<br/>
<a NAME="E4:37_1"/><span class="lab"><font color="Green" title="E29">A13</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></span>;<br/>
<a NAME="E5:37_1"/><span class="lab"><font color="Green" title="E30">A14</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></span>;<br/>
<a NAME="E6:37_1"/><span class="lab"><font color="Green" title="E31">A15</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></span>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="partfun2.html#T35" title="PARTFUN2:th.35">PARTFUN2:35</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="partfun2.html#T35" title="PARTFUN2:th.35">PARTFUN2:35</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="partfun2.html#T35" title="PARTFUN2:th.35">PARTFUN2:35</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37_1"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37_1"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:37"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E3:37_1"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E5:37_1"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="ref" href="funct_8.html#D3" target="_self" title="FUNCT_8:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E4:37_1"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E6:37_1"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="ref" href="funct_8.html#D3" target="_self" title="FUNCT_8:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_1"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37_1"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="partfun2.html#T35" title="PARTFUN2:th.35">PARTFUN2:35</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="partfun2.html#T35" title="PARTFUN2:th.35">PARTFUN2:35</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="partfun2.html#T35" title="PARTFUN2:th.35">PARTFUN2:35</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:37_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E11:37"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font> is  <a href="funct_8.html#V2" title="FUNCT_8:attr.2">with_symmetrical_domain</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Maroon" title="c1">A</font> is  <a href="funct_8.html#V3" title="FUNCT_8:attr.3">quasi_even</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="ref" href="funct_8.html#D2" target="_self" title="FUNCT_8:def.2">Def2</a>, <a class="ref" href="funct_8.html#D3" target="_self" title="FUNCT_8:def.3">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:37"/>
<font color="Maroon" title="c2">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c3">G</font> <a href="funct_8.html#R1" title="FUNCT_8:pred.1">is_even_on</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="funct_8.html#D5" target="_self" title="FUNCT_8:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
