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<span class="kw">let </span><font color="Maroon" title="c1">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="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">X1</font>, <font color="Olive" title="b3">X2</font> being    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b4">A</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c1">S</font> holds  <font color="Olive" title="b2">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b4">A</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b3">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b4">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">X1</font>, <font color="Olive" title="b2">X2</font> being    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</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="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c1">S</font> holds  <font color="Olive" title="b1">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b3">A</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b2">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b3">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">X1</font>, <font color="Maroon" title="c4">X2</font> be    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b1">A</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">A</font> be   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c1">S</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span><br/>







<span class="kw">thus </span><a NAME="E1:33"/>
(  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a></span>)</span> &amp;  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#T6" target="_self" onmouseover="rs('circtrm1/T6')" onmouseout="rh()">Th6</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="circcomb.html#D1" onmouseover="rs('circcomb/D1')" onmouseout="rh()">CIRCCOMB:def 1</a>,<a class="ref" href="circcomb.html#D3" onmouseover="rs('circcomb/D3')" onmouseout="rh()">CIRCCOMB:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <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 <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> &amp;  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E2:33"/>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <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 <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span>
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span></span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="33_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="partfun1.html#D4" onmouseover="rs('partfun1/D4')" onmouseout="rh()">PARTFUN1:def 4</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span></span>)</span> or  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:33_1"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span><br/>

<a NAME="E2:33_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E3:33_1"/><span class="lab"><font color="Green" title="E22">A3</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E4:33_1"/><span class="lab"><font color="Green" title="E23">A4</font></span>: 
<font color="Maroon" title="c6">x</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 <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33_1"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">v1</font> = <font color="Maroon" title="c6">x</font> as   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33_1"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">v2</font> = <font color="Maroon" title="c6">x</font> as   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33_1"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">t</font> = <font color="Maroon" title="c6">x</font> as   <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:33_1"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="circtrm1.html#T4" target="_self" onmouseover="rs('circtrm1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<span class="kw">thus </span> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
 <a href="circtrm1.html#K2" title="CIRCTRM1:func.2">the_sort_of</a> (<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">A</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#D4" target="_self" onmouseover="rs('circtrm1/D4')" onmouseout="rh()">Def4</a></span>
<br/>.= 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msaterm.html#K7" title="MSATERM:func.7">the_sort_of</a> <font color="Maroon" title="c9">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#D2" target="_self" onmouseover="rs('circtrm1/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
 <a href="circtrm1.html#K2" title="CIRCTRM1:func.2">the_sort_of</a> (<font color="Maroon" title="c8">v2</font>,<font color="Maroon" title="c5">A</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#D2" target="_self" onmouseover="rs('circtrm1/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#D4" target="_self" onmouseover="rs('circtrm1/D4')" onmouseout="rh()">Def4</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="partfun1.html#D4" onmouseover="rs('partfun1/D4')" onmouseout="rh()">PARTFUN1:def 4</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span></span>)</span> or  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:33"/><span class="lab"><font color="Green" title="E20">A5</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span><br/>

<a NAME="E4:33"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A6</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E5:33"/><span class="lab"><font color="Green" title="E22">A7</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">g1</font> = <font color="Maroon" title="c6">x</font> as   <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:33"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">g2</font> = <font color="Maroon" title="c6">x</font> as   <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:33"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">thus </span> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
 <a href="circtrm1.html#K3" title="CIRCTRM1:func.3">the_action_of</a> (<font color="Maroon" title="c7">g1</font>,<font color="Maroon" title="c5">A</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#D5" target="_self" onmouseover="rs('circtrm1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
 the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#D3" target="_self" onmouseover="rs('circtrm1/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
 <a href="circtrm1.html#K3" title="CIRCTRM1:func.3">the_action_of</a> (<font color="Maroon" title="c8">g2</font>,<font color="Maroon" title="c5">A</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#D3" target="_self" onmouseover="rs('circtrm1/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
 the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#D5" target="_self" onmouseover="rs('circtrm1/D5')" onmouseout="rh()">Def5</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
