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<b>let </b><font color="Maroon" title="c1">IIG</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="group_1.html#V6" title="GROUP_1:attr.6">finite</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a> <a href="msafree2.html#V5" title="MSAFREE2:attr.5">monotonic</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c1">IIG</font>;<br/><b>let </b><font color="Maroon" title="c3">v</font> be   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <font color="Maroon" title="c1">IIG</font>;<br/>





<b>consider </b><font color="Maroon" title="c4">Ds</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E2:30"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c4">Ds</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="circuit1.html#K6" title="CIRCUIT1:func.6">depth</a> <font color="Olive" title="b1">v'</font>,<font color="Maroon" title="c2">A</font></span>)</span> where <font color="Olive" title="b1">v'</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">IIG</font> : <font color="Olive" title="b1">v'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">IIG</font> </span>}</span> 
 <b>and </b><br/><a NAME="E3:30"/><i><font color="Green" title="E16">A2</font></i>: 
 <a href="circuit1.html#K7" title="CIRCUIT1:func.7">depth</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">max</a> <font color="Maroon" title="c4">Ds</font>
 <b>by </b><i><a class="ref" href="circuit1.html#D7" target="_self" title="CIRCUIT1:def.7">Def7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">Y</font> = <font color="Maroon" title="c4">Ds</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="membered.html#V2" title="MEMBERED:attr.2">real-membered</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<a NAME="E5:30"/>
 <a href="circuit1.html#K6" title="CIRCUIT1:func.6">depth</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font>
 
<b>by </b><i><a class="txt" href="circuit1.html#E2:30"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:30"/>
 <a href="circuit1.html#K6" title="CIRCUIT1:func.6">depth</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c2">A</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="circuit1.html#K7" title="CIRCUIT1:func.7">depth</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="circuit1.html#E3:30"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="pre_circ.html#D1" title="PRE_CIRC:def.1">PRE_CIRC:def 1</a></i>;<br/>


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