<?xml version="1.0"?>
<div class="add">

<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>, <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>let </b><font color="Maroon">C1</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S1</font>;<br/><b>let </b><font color="Maroon">C2</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S2</font>;<br/><b>let </b><font color="Maroon">C3</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S3</font>;<br/>









<b>assume </b><a NAME="E1:66"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">f1</font>,<font color="Maroon">g1</font> <a href="circtrm1.html#R4" target="_self">form_embedding_of</a> <font color="Maroon">C1</font>,<font color="Maroon">C2</font> &amp; <font color="Maroon">f1</font> <a href="funct_1.html#K2">"</a> ,<font color="Maroon">g1</font> <a href="funct_1.html#K2">"</a>  <a href="circtrm1.html#R4" target="_self">form_embedding_of</a> <font color="Maroon">C2</font>,<font color="Maroon">C1</font> &amp; <font color="Maroon">f2</font>,<font color="Maroon">g2</font> <a href="circtrm1.html#R4" target="_self">form_embedding_of</a> <font color="Maroon">C2</font>,<font color="Maroon">C3</font> &amp; <font color="Maroon">f2</font> <a href="funct_1.html#K2">"</a> ,<font color="Maroon">g2</font> <a href="funct_1.html#K2">"</a>  <a href="circtrm1.html#R4" target="_self">form_embedding_of</a> <font color="Maroon">C3</font>,<font color="Maroon">C2</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D13" target="_self">CIRCTRM1:def 13</a><br/>

<b>hence </b><a NAME="E2:66"/>
<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="circtrm1.html#R4" target="_self">form_embedding_of</a> <font color="Maroon">C1</font>,<font color="Maroon">C3</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D13" target="_self">CIRCTRM1:def 13</a><br/>

<a NAME="E3:66"/>
( <font color="Maroon">f1</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">g1</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">f2</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">g2</font> is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i><a class="ref" href="circtrm1.html#T2" target="_self">Th2</a>, </i>;<br/>
<a NAME="E4:66"/><b>then </b>
( <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> <a href="funct_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K2">"</a> </span>)</span> <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#K2">"</a> </span>)</span> &amp; <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="funct_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">g1</font> <a href="funct_1.html#K2">"</a> </span>)</span> <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#K2">"</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T66">FUNCT_1:66</a></i>;<br/>
<b>hence </b><a NAME="E5:66"/>
<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> <a href="funct_1.html#K2">"</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> <a href="funct_1.html#K2">"</a>  <a href="circtrm1.html#R4" target="_self">form_embedding_of</a> <font color="Maroon">C3</font>,<font color="Maroon">C1</font>
 <b>by </b><i><a class="ref" href="circtrm1.html#T2" target="_self">Th2</a>, </i>;<br/>


</div>
