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<span class="kw">let </span><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font>, <font color="Maroon" title="c3">S3</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A1</font> being  <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="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">A3</font> being  <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="c3">S3</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Olive" title="b2">A2</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Olive" title="b3">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A2</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Olive" title="b3">A3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">A1</font> be   <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A2</font> being  <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">A3</font> being  <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="c3">S3</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Olive" title="b1">A2</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Olive" title="b2">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A2</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Olive" title="b2">A3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">A2</font> be   <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A3</font> being  <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="c3">S3</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Olive" title="b1">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">A2</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Olive" title="b1">A3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">A3</font> be   <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="c3">S3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c6">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">A2</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c6">A3</font></span>)</span></span><br/>







<a NAME="E1:50"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c6">A3</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">A1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T67" title="CIRCCOMB:th.67">CIRCCOMB:67</a></span>;<br/>
<a NAME="E2:50"/>
( the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">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="c5">A2</font> &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A2</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="c6">A3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T67" title="CIRCCOMB:th.67">CIRCCOMB:67</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:50"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c6">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">A2</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c6">A3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="circcomb.html#T27" title="CIRCCOMB:th.27">CIRCCOMB:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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