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<b>let </b><font color="Maroon">IIG</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="msafree2.html#V5">monotonic</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">SCS</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">IIG</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="msafree2.html#NM1">Vertex</a> of <font color="Maroon">IIG</font>;<br/><b>let </b><font color="Maroon">iv</font> be    <a href="msafree2.html#M1">InputValues</a> of <font color="Maroon">SCS</font>;<br/>







<b>consider </b><font color="Maroon">e</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font><b> such that </b><br/><a NAME="E2:12"/><i><font color="Green">E42</font></i>: 
(  <a href="card_1.html#K4">card</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="circuit1.html#K4">size</a> <font color="Maroon">v</font>,<font color="Maroon">SCS</font> &amp;  <a href="circuit2.html#K4" target="_self">IGTree</a> <font color="Maroon">v</font>,<font color="Maroon">iv</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circuit2.html#K3" target="_self">Fix_inp_ext</a> <font color="Maroon">iv</font></span>)</span> <a href="msualg_3.html#K1">.</a> <font color="Maroon">v</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">e</font> )
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">igt</font> =  <a href="circuit2.html#K4" target="_self">IGTree</a> <font color="Maroon">v</font>,<font color="Maroon">iv</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> ;<br/>
<a NAME="E4:12"/>
 <a href="card_1.html#K4">card</a> <font color="Maroon">igt</font> <a href="hidden.html#R1">=</a>  <a href="circuit1.html#K4">size</a> <font color="Maroon">v</font>,<font color="Maroon">SCS</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:12"/>
 <a href="circuit2.html#K4" target="_self">IGTree</a> <font color="Maroon">v</font>,<font color="Maroon">iv</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circuit2.html#K3" target="_self">Fix_inp_ext</a> <font color="Maroon">iv</font></span>)</span> <a href="msualg_3.html#K1">.</a> <font color="Maroon">v</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="circuit2.html#K4" target="_self">IGTree</a> <font color="Maroon">v</font>,<font color="Maroon">iv</font></span>)</span>
 <b>by </b><i/>;<br/>


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