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<b>let </b><font color="Maroon" title="c3">F</font>, <font color="Maroon" title="c4">G</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">D</font>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:17_1_2"/><i><font color="Green" title="E11">A3</font></i>: 
for <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font><br/> for <font color="Olive" title="b2">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>   st <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> holds <br/><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b2">p</font>
 ;<br/>

<b>assume </b><a NAME="E2:17_1_2"/><i><font color="Green" title="E12">A4</font></i>: 
for <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font><br/> for <font color="Olive" title="b2">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>   st <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> holds <br/><font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b2">p</font>
 ;<br/>

<b>thus </b><a NAME="E3:17_1_2"/>
<font color="Maroon" title="c3">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">G</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_1_2_1"/>
for <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> holds  <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font>;<br/>

<b>consider </b><font color="Maroon" title="c6">p</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> <b> such that </b><br/><a NAME="E2:17_1_2_1_1"/><i><font color="Green" title="E13">A5</font></i>: 
<font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font>
 ;<br/>
<b>thus </b><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font> = 
 <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c6">p</font>
<b>by </b><i><a class="txt" href="cqc_sim1.html#E1:17_1_2"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="cqc_sim1.html#E2:17_1_2_1_1"><i><font color="Green" title="E13">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="txt" href="cqc_sim1.html#E2:17_1_2"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="cqc_sim1.html#E2:17_1_2_1_1"><i><font color="Green" title="E13">A5</font></i></a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:17_1_2_1"/>
<font color="Maroon" title="c3">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


</div><b>end;</b></div>


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