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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><a NAME="E1:79"/>
<font color="Maroon">C1</font>,<font color="Maroon">C2</font> <a href="circtrm1.html#R5" target="_self">are_similar_wrt</a> <font color="Maroon">f</font>,<font color="Maroon">g</font>
 ;<br/>

<a NAME="E2:79"/><b>then </b>
<font color="Maroon">G1</font>,<font color="Maroon">G2</font> <a href="circtrm1.html#R1" target="_self">are_equivalent_wrt</a> <font color="Maroon">f</font>,<font color="Maroon">g</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:79"/>
( <font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">G1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">G2</font> &amp; <font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">G1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">G2</font> )
 <b>by </b><i/>;<br/>


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