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<b>let </b><font color="Maroon">S1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> , <font color="Maroon">S2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> , <font color="Maroon">S3</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g1</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>assume </b><a NAME="E1:37"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">f1</font>,<font color="Maroon">g1</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">S1</font>,<font color="Maroon">S2</font>
 ;<br/>

<b>let </b><font color="Maroon">f2</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g2</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E2:37"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">f2</font>,<font color="Maroon">g2</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">S2</font>,<font color="Maroon">S3</font>
 ;<br/>

<b>let </b><font color="Maroon">A</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S3</font>;<br/>

<a NAME="E3:37"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">f2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f1</font>,<font color="Maroon">g2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">S1</font>,<font color="Maroon">S3</font>
 
<b>by </b><i>, , <a class="ref" href="pua2mss1.html#T30">PUA2MSS1:30</a></i>;<br/>
<i><font color="Green">E53</font></i>: the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S2</font>,<font color="Maroon">f2</font>,<font color="Maroon">g2</font></span>)</span> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S1</font>,<font color="Maroon">f1</font>,<font color="Maroon">g1</font></span>)</span> = 
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S2</font>,<font color="Maroon">f2</font>,<font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f1</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f2</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f1</font>
<b>by </b><i>, </i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f1</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
;<br/>
the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S2</font>,<font color="Maroon">f2</font>,<font color="Maroon">g2</font></span>)</span> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S1</font>,<font color="Maroon">f1</font>,<font color="Maroon">g1</font></span>)</span> = 
the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S2</font>,<font color="Maroon">f2</font>,<font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font>
<b>by </b><i>, </i>
<br/>.= 
the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
;<br/>
<b>hence </b><a NAME="E6:37"/>
<font color="Maroon">A</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S1</font>,<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font></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>,<font color="Maroon">f2</font>,<font color="Maroon">g2</font></span>)</span> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S1</font>,<font color="Maroon">f1</font>,<font color="Maroon">g1</font>
 <b>by </b><i>, , </i>;<br/>


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