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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:70"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="funct_1.html#V2">one-to-one</a> )
 <b>and </b><br/><a NAME="E2:70"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E3:70"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:70"/>
the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>4</sub></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">c<sub>7</sub></font> be   <a href="circcomb.html#NM1">Gate</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="circcomb.html#NM1">Gate</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>



<b>assume </b><a NAME="E5:70"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">c<sub>5</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">c<sub>6</sub></font>;<br/>



<b>assume </b><a NAME="E6:70"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>thus </b><font color="Maroon">c<sub>8</sub></font> <a href="circuit1.html#K3">depends_on_in</a> <font color="Maroon">c<sub>10</sub></font> = 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="circuit1.html#D3">CIRCUIT1:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="circtrm1.html#E2:70"><i><font color="Green">E47</font></i></a>, <a class="txt" href="circtrm1.html#E5:70"><i><font color="Green">E48</font></i></a>, <a class="ref" href="pua2mss1.html#D13">PUA2MSS1:def 13</a></i>
<br/>.= 
<font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="circtrm1.html#E6:70"><i><font color="Green">E49</font></i></a>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="circuit1.html#K3">depends_on_in</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="circuit1.html#D3">CIRCUIT1:def 3</a></i>
;<br/>


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