<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</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="circcomb.html#V1" title="CIRCCOMB:attr.1">unsplit</a> <a href="circcomb.html#V2" title="CIRCCOMB:attr.2">gate`1=arity</a> <a href="circcomb.html#V3" title="CIRCCOMB:attr.3">gate`2isBoolean</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"> 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="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a> <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</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="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a> <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</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">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Olive" title="b2">A2</font></span>)</span> holds <br/> ( <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="c1">S1</font> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">A1</font> &amp; <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> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">A2</font> )</span><br/><b>let </b><font color="Maroon" title="c3">A1</font> be  <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a> <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</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="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a> <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</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">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Olive" title="b1">A2</font></span>)</span> holds <br/> ( <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="c1">S1</font> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c3">A1</font> &amp; <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> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">A2</font> )</span><br/><b>let </b><font color="Maroon" title="c4">A2</font> be  <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a> <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</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">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c4">A2</font></span>)</span> holds <br/> ( <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="c1">S1</font> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c3">A1</font> &amp; <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> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">A2</font> )</span><br/><b>let </b><font color="Maroon" title="c5">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c4">A2</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">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="c1">S1</font> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c3">A1</font> &amp; <font color="Maroon" title="c5">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> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">A2</font> )</span><br/>







<a NAME="E1:52"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A2</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#T67" title="CIRCCOMB:th.67">CIRCCOMB:67</a></i>;<br/>
<b>hence </b><a NAME="E2:52"/>
( <font color="Maroon" title="c5">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="c1">S1</font> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c3">A1</font> &amp; <font color="Maroon" title="c5">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> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">A2</font> )
 <b>by </b><i><a class="ref" href="circcomb.html#T33" title="CIRCCOMB:th.33">CIRCCOMB:33</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
