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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="funct_1.html#NM1">Function</a>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="margrel1.html#K6">BOOLEAN</a>  =  <a href="margrel1.html#K12">ALL</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Olive">v'</font></span>)</span> where <font color="Olive">v'</font> is    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font> : for <font color="Olive">y</font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a>  st <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">y</font> holds <br/><font color="Olive">v'</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">y</font> </span>}</span> ;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font>, <a href="margrel1.html#K6">BOOLEAN</a> <b> such that </b><br/><a NAME="E2:11_1_1"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">v</font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">v</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i>
<a NAME="E3:11_1_1"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="margrel1.html#K6">BOOLEAN</a>  )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a>  <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E5:11_1_1"/>
for <font color="Olive">v</font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K12">ALL</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Olive">v'</font></span>)</span> where <font color="Olive">v'</font> is    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font> : for <font color="Olive">y</font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a>  st <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">y</font> holds <br/><font color="Olive">v'</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">v</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> </span>}</span> 
 <b>by </b><i/>;<br/>


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