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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  <span class="p1">(<span class="default"><font color="Olive" title="b2">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">X2</font></span>)</span> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <span class="p1">(<span class="default"><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>)</span></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  <span class="p1">(<span class="default"><font color="Olive" title="b1">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">X2</font></span>)</span> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <span class="p1">(<span class="default"><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>)</span></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  <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="Olive" title="b1">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="Olive" title="b1">A</font></span>)</span></span><br/>





<span class="kw">consider </span><font color="Maroon" title="c5">t1</font> being    <a href="msaterm.html#M2" title="MSATERM:mode.2">CompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font><span class="kw"> such that </span><br/><a NAME="E2:34"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon" title="c5">t1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">X1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msaterm.html#D7" onmouseover="rs('msaterm/D7')" onmouseout="rh()">MSATERM:def 7</a></span>;<br/>
<a NAME="E3:34"/>
<font color="Maroon" title="c5">t1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">X2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">X</font> = <font color="Maroon" title="c3">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">X2</font> as    <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> <span class="kw">by</span> <span class="lab"><a class="ref" href="msaterm.html#D7" onmouseover="rs('msaterm/D7')" onmouseout="rh()">MSATERM:def 7</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">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"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c7">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="c7">A</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">C1</font> = <font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">C2</font> = <font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">C</font> = <font color="Maroon" title="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font>;<br/>
<a NAME="E5:34"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">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="c7">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#T18" target="_self" onmouseover="rs('circtrm1/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E6:34"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A3</font></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="c7">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="c7">A</font></span>)</span>
 
;<br/>
<a NAME="E7:34"/><span class="lab"><font color="Green" title="E23">A4</font></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="c7">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="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:34"><span class="lab"><font color="Green" title="E21">A2</font></span></a></span>;<br/>
<a NAME="E8:34"/><span class="lab"><font color="Green" title="E24">A5</font></span>: 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><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="c7">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="c7">A</font></span>)</span></span>)</span> <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="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.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="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:34"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="circcomb.html#D4" onmouseover="rs('circcomb/D4')" onmouseout="rh()">CIRCCOMB:def 4</a></span>;<br/>
<a NAME="E9:34"/><span class="lab"><font color="Green" title="E25">A6</font></span>: 
 the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><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="c7">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="c7">A</font></span>)</span></span>)</span> <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="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.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="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:34"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="circcomb.html#D4" onmouseover="rs('circcomb/D4')" onmouseout="rh()">CIRCCOMB:def 4</a></span>;<br/>
<a NAME="E10:34"/><span class="lab"><font color="Green" title="E26">A7</font></span>: 
<font color="Maroon" title="c6">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <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#T10" target="_self" onmouseover="rs('circtrm1/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<a NAME="E11:34"/><span class="lab"><font color="Green" title="E27">A8</font></span>: 
<font color="Maroon" title="c3">X1</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#T18" target="_self" onmouseover="rs('circtrm1/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E12:34"/><span class="lab"><font color="Green" title="E28">A9</font></span>: 
<font color="Maroon" title="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#T18" target="_self" onmouseover="rs('circtrm1/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E13:34"/><span class="lab"><font color="Green" title="E29">A10</font></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="c7">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="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:34"><span class="lab"><font color="Green" title="E27">A8</font></span></a></span>;<br/>
<a NAME="E14:34"/><span class="lab"><font color="Green" title="E30">A11</font></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="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">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="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:34"><span class="lab"><font color="Green" title="E28">A9</font></span></a></span>;<br/>
<a NAME="E15:34"/><span class="lab"><font color="Green" title="E31">A12</font></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="c7">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="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:34"><span class="lab"><font color="Green" title="E27">A8</font></span></a></span>;<br/>
<a NAME="E16:34"/><span class="lab"><font color="Green" title="E32">A13</font></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="c4">X2</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">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="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:34"><span class="lab"><font color="Green" title="E28">A9</font></span></a></span>;<br/>
<a NAME="E17:34"/><span class="lab"><font color="Green" title="E33">A14</font></span>: 
 <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"><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="c7">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="c7">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c6">X</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="#E10:34"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E18:34"/>
 <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"><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="c7">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="c7">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">X</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="#E10:34"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E19:34"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A15</font></span>: 
 <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"><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="c7">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="c7">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E20:34"/><span class="lab"><font color="Green" title="E35">A16</font></span>: 
 <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"><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="c7">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="c7">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:34"><span class="lab"><font color="Green" title="E33">A14</font></span></a>, <a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E21:34"/><span class="lab"><font color="Green" title="E36">A17</font></span>: 
 the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><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="c7">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="c7">A</font></span>)</span></span>)</span> <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="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:34"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E9:34"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E15:34"><span class="lab"><font color="Green" title="E31">A12</font></span></a>, <a class="txt" href="#E16:34"><span class="lab"><font color="Green" title="E32">A13</font></span></a>, <a class="txt" href="#E19:34"><span class="lab"><font color="Green" title="E34">A15</font></span></a>, <a class="ref" href="funct_4.html#T125" onmouseover="rs('funct_4/T125')" onmouseout="rh()">FUNCT_4:125</a>, <a class="ref" href="partfun1.html#T55" onmouseover="rs('partfun1/T55')" onmouseout="rh()">PARTFUN1:55</a></span>;<br/>
<a NAME="E22:34"/>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><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="c7">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="c7">A</font></span>)</span></span>)</span> <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="c6">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:34"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="txt" href="#E8:34"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E13:34"><span class="lab"><font color="Green" title="E29">A10</font></span></a>, <a class="txt" href="#E14:34"><span class="lab"><font color="Green" title="E30">A11</font></span></a>, <a class="txt" href="#E20:34"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="ref" href="funct_4.html#T125" onmouseover="rs('funct_4/T125')" onmouseout="rh()">FUNCT_4:125</a>, <a class="ref" href="partfun1.html#T55" onmouseover="rs('partfun1/T55')" onmouseout="rh()">PARTFUN1:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E23:34"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c7">A</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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="c7">A</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:34"><span class="lab"><font color="Green" title="E36">A17</font></span></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>
