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<b>let </b><font color="Maroon">G1</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a> <a href="msafree2.html#V2">Circuit-like</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">G2</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a> <a href="msafree2.html#V2">Circuit-like</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">g</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="circuit1.html#NM1">Circuit</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">C2</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">G2</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:69"/>
( <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">g</font> is <a href="funct_1.html#V2">one-to-one</a> )
 <b>and </b><br/><a NAME="E2:69"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">G1</font>,<font color="Maroon">G2</font>
 <b>and </b><br/><a NAME="E3:69"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">C2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E4:69"/><i><font color="Green">E39</font></i>: 
the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">C2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D12" target="_self">CIRCTRM1:def 12</a><br/>

<b>let </b><font color="Maroon">o1</font> be   <a href="circcomb.html#NM1">Gate</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">o2</font> be   <a href="circcomb.html#NM1">Gate</a> of <font color="Maroon">G2</font>;<br/>



<b>assume </b><a NAME="E5:69"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">o2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o1</font>
 ;<br/>

<a NAME="E6:69"/><i><font color="Green">E65</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">G1</font>
 
<b>by </b><i><a class="ref" href="circtrm1.html#T3" target="_self">Th3</a>, <a class="ref" href="pua2mss1.html#D13">PUA2MSS1:def 13</a></i>;<br/>
<b>thus </b><a NAME="E7:69"/>
 <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o2</font>,<font color="Maroon">C2</font> <a href="funct_2.html#R1">=</a>  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o1</font>,<font color="Maroon">C1</font>
 <b>by </b><i><a class="ref" href="circtrm1.html#T4" target="_self">Th4</a>, , <a class="ref" href="circtrm1.html#T5" target="_self">Th5</a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/>


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