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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">V</font> be  <a href="relat_1.html#V2">V5</a>  <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">X1</font> be    <a href="msaterm.html#M3">SetWithCompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>, <font color="Maroon">X2</font> be    <a href="msaterm.html#M3">SetWithCompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>;<br/>





<b>consider </b><font color="Maroon">t1</font> being    <a href="msaterm.html#M2">CompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:35"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">t1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font>
 <b>by </b><i><a class="ref" href="msaterm.html#D7">MSATERM:def 7</a></i>;<br/>
<a NAME="E3:35"/>
<font color="Maroon">t1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">X2</font>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">X</font> = <font color="Maroon">X1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">X2</font> as    <a href="msaterm.html#M3">SetWithCompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font> <b>by </b><i><a class="ref" href="msaterm.html#D7">MSATERM:def 7</a></i>;<br/>
<b>let </b><font color="Maroon">A</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/>

<b>set </b><font color="Maroon">C1</font> = <font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font>;<br/>
<b>set </b><font color="Maroon">C2</font> = <font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font>;<br/>
<b>set </b><font color="Maroon">C</font> = <font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font>;<br/>
<a NAME="E5:35"/>
<font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font> <a href="circcomb.html#R2">tolerates</a> <font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:35"/><b>then </b><i><font color="Green">E39</font></i>: 
( the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> &amp; the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="circcomb.html#D3">CIRCCOMB:def 3</a></i>;<br/>
<a NAME="E7:35"/><b>then </b><i><font color="Green">E42</font></i>: 
( the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K1">+*</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> &amp; the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K1">+*</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="circcomb.html#D4">CIRCCOMB:def 4</a></i>;<br/>
<a NAME="E8:35"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">X</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span> <a href="circcomb.html#K3">+*</a> <span class="p1">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E9:35"/>
( <font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font> <a href="circcomb.html#R2">tolerates</a> <font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font> &amp; <font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font> <a href="circcomb.html#R2">tolerates</a> <font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E10:35"/><b>then </b>
( the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> &amp; the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> &amp; the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="circcomb.html#D3">CIRCCOMB:def 3</a></i>;<br/>
<a NAME="E11:35"/><b>then </b><i><font color="Green">E71</font></i>: 
( the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> &amp; the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i>, , <a class="ref" href="circcomb.html#T5">CIRCCOMB:5</a></i>;<br/>
<a NAME="E12:35"/>
(  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span> )
 
<b>by </b><i>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E13:35"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E14:35"/><b>then </b>
( the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="partfun1.html#T136">PARTFUN1:136</a></i>;<br/>
<b>hence </b><a NAME="E15:35"/>
<span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">X2</font></span>)</span> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p1">(<span class="default"><font color="Maroon">X2</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span>
 ;<br/>


</div>
