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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be  non <a href="msualg_1.html#V2">void</a>  <a href="instalg1.html#M1" target="_self">Subsignature</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:45"/><i><font color="Green">E25</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>3</sub></font> <a href="pzfmisc1.html#R1">is_transformable_to</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>

<b>assume </b><a NAME="E2:45"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E3:45"/><i><font color="Green">E27</font></i>: 
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>, <a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="instalg1.html#D2" target="_self">Def2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> =  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="instalg1.html#T10" target="_self">Th10</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></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">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></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">c<sub>2</sub></font></span>)</span></span>)</span><b> such that </b><br/><a NAME="E6:45"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">c<sub>3</sub></font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></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">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></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">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="instalg1.html#E1:45"><i><font color="Green">E25</font></i></a>, <a class="txt" href="instalg1.html#E2:45"><i><font color="Green">E26</font></i></a>, <a class="txt" href="instalg1.html#E3:45"><i><font color="Green">E27</font></i></a>, <a class="ref" href="instalg1.html#T35" target="_self">Th35</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span><b> such that </b><br/><a NAME="E8:45"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">c<sub>3</sub></font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="instalg1.html#E6:45"><i><font color="Green">E28</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>10</sub></font>
;<br/>

<b>thus </b><a NAME="E9:45"/>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">c<sub>3</sub></font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="instalg1.html#E6:45"><i><font color="Green">E28</font></i></a>, <a class="txt" href="instalg1.html#E8:45"><i><font color="Green">E29</font></i></a>, <a class="ref" href="relat_1.html#T94">RELAT_1:94</a></i>;<br/>


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