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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font>, <font color="Maroon" title="c3">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> implies for <font color="Olive" title="b1">A1</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c1">S1</font><br/> for <font color="Olive" title="b2">A2</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c2">S2</font><br/> for <font color="Olive" title="b3">A</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b4">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b3">A</font><br/> for <font color="Olive" title="b5">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">A2</font>  st <font color="Olive" title="b5">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b6">g</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b7">g2</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">g2</font> holds <br/><font color="Olive" title="b6">g</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">g2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b5">s2</font> )</span><br/>

<b>assume </b><a NAME="E1:47"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A1</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c1">S1</font><br/> for <font color="Olive" title="b2">A2</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c2">S2</font><br/> for <font color="Olive" title="b3">A</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b4">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b3">A</font><br/> for <font color="Olive" title="b5">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">A2</font>  st <font color="Olive" title="b5">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b6">g</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b7">g2</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">g2</font> holds <br/><font color="Olive" title="b6">g</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">g2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b5">s2</font></span><br/>

<b>let </b><font color="Maroon" title="c4">A1</font> be  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c1">S1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A2</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c2">S2</font><br/> for <font color="Olive" title="b2">A</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b3">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">A</font><br/> for <font color="Olive" title="b4">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">A2</font>  st <font color="Olive" title="b4">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b5">g</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b6">g2</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">g2</font> holds <br/><font color="Olive" title="b5">g</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">g2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b4">s2</font></span><br/><b>let </b><font color="Maroon" title="c5">A2</font> be  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c2">S2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b2">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b3">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>  st <font color="Olive" title="b3">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b4">g</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b5">g2</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">g2</font> holds <br/><font color="Olive" title="b4">g</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">g2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b3">s2</font></span><br/><b>let </b><font color="Maroon" title="c6">A</font> be  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c3">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">A</font><br/> for <font color="Olive" title="b2">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>  st <font color="Olive" title="b2">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b3">g</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b4">g2</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">g2</font> holds <br/><font color="Olive" title="b3">g</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">g2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b2">s2</font></span><br/><b>let </b><font color="Maroon" title="c7">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>  st <font color="Olive" title="b1">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b2">g</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b3">g2</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">g2</font> holds <br/><font color="Olive" title="b2">g</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">g2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Olive" title="b1">s2</font></span><br/><b>let </b><font color="Maroon" title="c8">s2</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> implies for <font color="Olive" title="b1">g</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b2">g2</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g2</font> holds <br/><font color="Olive" title="b1">g</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c8">s2</font> )</span><br/>









<b>assume </b><a NAME="E2:47"/><i><font color="Green" title="E30">A2</font></i>: 
<font color="Maroon" title="c8">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">g</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b2">g2</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g2</font> holds <br/><font color="Olive" title="b1">g</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c8">s2</font></span><br/>

<b>let </b><font color="Maroon" title="c9">o</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c3">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">g2</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c2">S2</font>  st <font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g2</font> holds <br/><font color="Maroon" title="c9">o</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c8">s2</font></span><br/><b>let </b><font color="Maroon" title="c10">o2</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">o2</font> implies <font color="Maroon" title="c9">o</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">o2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c8">s2</font> )</span><br/>



<b>assume </b><a NAME="E3:47"/><i><font color="Green" title="E31">A3</font></i>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">o2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">o</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">o2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c8">s2</font></span><br/>

<a NAME="E4:47"/>
( <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font></span>)</span></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a>, <a class="ref" href="relat_1.html#T125" title="RELAT_1:th.125">RELAT_1:125</a></i>;<br/>
<a NAME="E5:47"/><b>then </b>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font> &amp;  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T117" title="RELAT_1:th.117">RELAT_1:117</a>, <a class="ref" href="relat_1.html#T131" title="RELAT_1:th.131">RELAT_1:131</a></i>;<br/>
<a NAME="E6:47"/><b>then </b><i><font color="Green" title="E32">A4</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c9">o</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c7">s</font> = 
<font color="Maroon" title="c7">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c9">o</font></span>)</span>
<b>by </b><i><a class="ref" href="circuit1.html#D3" title="CIRCUIT1:def.3">CIRCUIT1:def 3</a></i>
<br/>.= 
<font color="Maroon" title="c7">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:47"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="#E3:47"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="circcomb.html#T18" target="_self" title="CIRCCOMB:th.18">Th18</a></i>
<br/>.= 
<font color="Maroon" title="c8">s2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:47"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="#E6:47"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="monoid_1.html#T2" title="MONOID_1:th.2">MONOID_1:2</a></i>
<br/>.= 
<font color="Maroon" title="c10">o2</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c8">s2</font>
<b>by </b><i><a class="ref" href="circuit1.html#D3" title="CIRCUIT1:def.3">CIRCUIT1:def 3</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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