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<b>let </b><font color="Maroon">S1</font> be  non <a href="struct_0.html#V3">empty</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">S2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="instalg1.html#M1" target="_self">Subsignature</a> of <font color="Maroon">S1</font>;<br/><b>let </b><font color="Maroon">S3</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="instalg1.html#M1" target="_self">Subsignature</a> of <font color="Maroon">S2</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S1</font>;<br/>







<b>set </b><font color="Maroon">f1</font> =  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font>;<br/>
<b>set </b><font color="Maroon">g1</font> =  <a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font>;<br/>
<b>set </b><font color="Maroon">f2</font> =  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S3</font>;<br/>
<b>set </b><font color="Maroon">g2</font> =  <a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S3</font>;<br/>
<a NAME="E1:38"/>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S3</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S3</font> &amp;  <a href="relat_1.html#K2">rng</a> <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">S3</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S3</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S3</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S3</font> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> )
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<a NAME="E2:38"/><b>then </b><i><font color="Green">E37</font></i>: 
( <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S3</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S3</font> &amp; <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">S2</font></span>)</span> <a href="partfun1.html#K1">*</a> <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">S3</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S3</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T79">RELAT_1:79</a></i>;<br/>
<a NAME="E3:38"/>
(  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font>, <a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">S2</font>,<font color="Maroon">S1</font> &amp;  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S3</font>, <a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S3</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">S3</font>,<font color="Maroon">S2</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:38"/><b>then </b>
<font color="Maroon">A</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S3</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S3</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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">S2</font></span>)</span> <a href="partfun1.html#K1">*</a> <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">S3</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S2</font>,<span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font></span>)</span>,<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">S2</font></span>)</span></span>)</span> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S3</font>,<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S3</font></span>)</span>,<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">S3</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:38"/>
<font color="Maroon">A</font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">S3</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">S2</font></span>)</span> <a href="instalg1.html#K2" target="_self">|</a> <font color="Maroon">S3</font>
 <b>by </b><i/>;<br/>


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