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<b>let </b><font color="Maroon">S</font> be  non <a href="msualg_1.html#V2">void</a> <a href="instalg1.html#V1" target="_self">feasible</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">S'</font> be  non <a href="msualg_1.html#V2">void</a>  <a href="instalg1.html#M1" target="_self">Subsignature</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">A1</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>, <font color="Maroon">A2</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/>





<b>assume </b><a NAME="E1:45"/><i><font color="Green">E37</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pzfmisc1.html#R1">is_transformable_to</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font>
 ;<br/>

<b>let </b><font color="Maroon">h</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">A1</font>,<font color="Maroon">A2</font>;<br/>

<b>assume </b><a NAME="E2:45"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">h</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">A1</font>,<font color="Maroon">A2</font>
 ;<br/>

<b>set </b><font color="Maroon">f</font> =  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S'</font>;<br/>
<b>set </b><font color="Maroon">g</font> =  <a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S'</font>;<br/>
<a NAME="E3:45"/><i><font color="Green">E52</font></i>: 
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S'</font>, <a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S'</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">S'</font>,<font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> =  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S'</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S'</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <b>by </b><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"><font color="Maroon">A1</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S'</font>,<font color="Maroon">f</font>,<span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S'</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">A2</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S'</font>,<font color="Maroon">f</font>,<span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S'</font></span>)</span></span>)</span><b> such that </b><br/><a NAME="E6:45"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">h'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">h</font> <a href="pboole.html#K7">*</a> <font color="Maroon">f</font> &amp; <font color="Maroon">h'</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">A1</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S'</font>,<font color="Maroon">f</font>,<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S'</font></span>)</span>,<font color="Maroon">A2</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S'</font>,<font color="Maroon">f</font>,<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S'</font></span>)</span> )
 <b>by </b><i>, , , </i>;<br/>
<b>consider </b><font color="Maroon">k</font> being   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">S'</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">A2</font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">S'</font></span>)</span><b> such that </b><br/><a NAME="E8:45"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">k</font> <a href="pboole.html#R6">=</a> <font color="Maroon">h'</font> &amp; <font color="Maroon">k</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">A1</font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">S'</font>,<font color="Maroon">A2</font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">S'</font> )
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">k</font>
;<br/>

<b>thus </b><a NAME="E9:45"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S'</font> &amp; <font color="Maroon">k</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">A1</font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">S'</font>,<font color="Maroon">A2</font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">S'</font> )
 <b>by </b><i>, , <a class="ref" href="relat_1.html#T94">RELAT_1:94</a></i>;<br/>


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