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<b>let </b><font color="Maroon" title="c7">F1</font>, <font color="Maroon" title="c8">F2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="eqrel_1.html#K9" title="EQREL_1:func.9">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>, <a href="eqrel_1.html#K9" title="EQREL_1:func.9">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:40_1_2"/><i><font color="Green" title="E30">A7</font></i>: 
for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font> holds  <font color="Maroon" title="c7">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p2">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>,<font color="Olive" title="b1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Olive" title="b1">p</font></span>)</span>
 <b>and </b><br/><a NAME="E2:40_1_2"/><i><font color="Green" title="E31">A8</font></i>: 
for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font> holds  <font color="Maroon" title="c8">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p2">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>,<font color="Olive" title="b1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Olive" title="b1">p</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:40_1_2_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K9" title="EQREL_1:func.9">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c10">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font><b> such that </b><br/><a NAME="E3:40_1_2_1"/><i><font color="Green" title="E32">A9</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>,<font color="Maroon" title="c10">p</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T45" title="EQREL_1:th.45">EQREL_1:45</a></i>;<br/><a NAME="E4:40_1_2_1"/>
( <font color="Maroon" title="c7">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p</font></span>)</span> &amp; <font color="Maroon" title="c8">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p</font></span>)</span> )
 <b>by </b><i><a class="txt" href="qmax_1.html#E1:40_1_2"><i><font color="Green" title="E30">A7</font></i></a>, <a class="txt" href="qmax_1.html#E2:40_1_2"><i><font color="Green" title="E31">A8</font></i></a>, <a class="txt" href="qmax_1.html#E3:40_1_2_1"><i><font color="Green" title="E32">A9</font></i></a></i>;<br/><b>hence </b><a NAME="E5:40_1_2_1"/>
<font color="Maroon" title="c7">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:40_1_2"/>
<font color="Maroon" title="c7">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">F2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</a></i>;<br/>


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