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<b>let </b><font color="Maroon" title="c5">C1</font>, <font color="Maroon" title="c6">C2</font> be    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K4" title="CIRCTRM1:func.4">-CircuitSorts</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K4" title="CIRCTRM1:func.4">-CircuitSorts</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> </span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:29_1_1"/><i><font color="Green" title="E18">A1</font></i>: 
for <font color="Olive" title="b1">o</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> </span>)</span>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> </span>)</span> holds <br/><font color="Maroon" title="c5">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circtrm1.html#K3" title="CIRCTRM1:func.3">the_action_of</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c4">A</font>
 <b>and </b><br/><a NAME="E2:29_1_1"/><i><font color="Green" title="E19">A2</font></i>: 
for <font color="Olive" title="b1">o</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> </span>)</span>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> </span>)</span> holds <br/><font color="Maroon" title="c6">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circtrm1.html#K3" title="CIRCTRM1:func.3">the_action_of</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c4">A</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:29_1_1_1"/><i><font color="Green" title="E20">A3</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> </span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c8">o</font> = <font color="Maroon" title="c7">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">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> </span>)</span> ;<br/><a NAME="E3:29_1_1_1"/>
( <font color="Maroon" title="c5">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circtrm1.html#K3" title="CIRCTRM1:func.3">the_action_of</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c6">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circtrm1.html#K3" title="CIRCTRM1:func.3">the_action_of</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c4">A</font> )
 <b>by </b><i><a class="txt" href="circtrm1.html#E1:29_1_1"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="circtrm1.html#E2:29_1_1"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="circtrm1.html#E1:29_1_1_1"><i><font color="Green" title="E20">A3</font></i></a></i>;<br/><b>hence </b><a NAME="E4:29_1_1_1"/>
<font color="Maroon" title="c5">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:29_1_1"/>
<font color="Maroon" title="c5">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">C2</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>;<br/>


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