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<b>reconsider </b><font color="Maroon">G</font> =  <a href="msafree.html#K13">FreeGen</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> as  <a href="msafree.html#V1">free</a>  <a href="msafree.html#M1">GeneratorSet</a> of  <a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font> <b>by </b><i><a class="ref" href="msafree.html#T17">MSAFREE:17</a></i>;<br/>
<b>consider </b><font color="Maroon">h</font> being   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span><b> such that </b><br/><a NAME="E3:4_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">h</font> <a href="msualg_3.html#R1">is_homomorphism</a>  <a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font>, <a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E4:4_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">h</font> <a href="msafree.html#K1">||</a> <font color="Maroon">G</font> <a href="pboole.html#R6">=</a>  <a href="circuit2.html#K2" target="_self">Fix_inp</a> <font color="Maroon">iv</font>
 <b>by </b><i><a class="ref" href="msafree.html#D5">MSAFREE:def 5</a></i>;<br/>
<b>take </b>
<font color="Maroon">h</font>
;<br/>

<b>thus </b><a NAME="E5:4_1_1"/>
<font color="Maroon">h</font> <a href="msualg_3.html#R1">is_homomorphism</a>  <a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font>, <a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D5">PBOOLE:def 5</a><br/>

<b>assume </b><a NAME="E6:4_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">IIG</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">hi</font> = <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>,the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <b>by </b><i><a class="ref" href="pboole.html#D18">PBOOLE:def 18</a></i>;<br/>
<a NAME="E8:4_1_1"/>
<span class="p1">(<span class="default"><a href="circuit2.html#K2" target="_self">Fix_inp</a> <font color="Maroon">iv</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">hi</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="msafree.html#D1">MSAFREE:def 1</a></i>;<br/>
<b>hence </b><a NAME="E9:4_1_1"/>
<span class="p1">(<span class="default"><a href="circuit2.html#K2" target="_self">Fix_inp</a> <font color="Maroon">iv</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T88">RELAT_1:88</a></i>;<br/>


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