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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S1</font>, <font color="Maroon" title="c3">S2</font> be    <a href="circcmb3.html#M1" title="CIRCCMB3:mode.1">Signature</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c4">A1</font> be    <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">S1</font>;<br/><b>let </b><font color="Maroon" title="c5">A2</font> be    <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">S2</font>;<br/>







<b>reconsider </b><font color="Maroon" title="c6">A</font> = <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c5">A2</font> as   <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c2">S1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c3">S2</font> <b>by </b><i><a class="ref" href="circcmb3.html#T31" target="_self" title="CIRCCMB3:th.31">Th31</a></i>;<br/>
<a NAME="E2:63"/>
<font color="Maroon" title="c4">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c5">A2</font>
 
<b>by </b><i><a class="ref" href="circcmb3.html#T30" target="_self" title="CIRCCMB3:th.30">Th30</a></i>;<br/>
<a NAME="E3:63"/><b>then </b><i><font color="Green" title="E32">A1</font></i>: 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">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#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#D3" title="CIRCCOMB:def.3">CIRCCOMB:def 3</a></i>;<br/>
<a NAME="E4:63"/>
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> &amp;  <a href="yellow_6.html#K1" title="YELLOW_6:func.1">the_value_of</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> &amp;  <a href="yellow_6.html#K1" title="YELLOW_6:func.1">the_value_of</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="ref" href="circcmb3.html#D10" target="_self" title="CIRCCMB3:def.10">Def10</a></i>;<br/>
<a NAME="E5:63"/><b>then </b>
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c1">X</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="ref" href="circcmb3.html#T23" target="_self" title="CIRCCMB3:th.23">Th23</a></i>;<br/>
<a NAME="E6:63"/><b>then </b><i><font color="Green" title="E33">A2</font></i>: 
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font></span>)</span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font></span>)</span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#D2" title="FUNCOP_1:def.2">FUNCOP_1:def 2</a></i>;<br/>
<a NAME="E7:63"/><i><font color="Green" title="E34">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font> <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 <font color="Maroon" title="c2">S1</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c6">A</font> = 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K1" title="CIRCCOMB:func.1">+*</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E3:63"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="circcomb.html#D4" title="CIRCCOMB:def.4">CIRCCOMB:def 4</a></i>
<br/>.= 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E3:63"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="funct_4.html#T31" title="FUNCT_4:th.31">FUNCT_4:31</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font></span>)</span></span>)</span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<b>by </b><i><a class="txt" href="circcmb3.html#E6:63"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T120" title="ZFMISC_1:th.120">ZFMISC_1:120</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font></span>)</span></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E7:63"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="funcop_1.html#D2" title="FUNCOP_1:def.2">FUNCOP_1:def 2</a></i>
;<br/>
<b>hence </b><a NAME="E9:63"/>
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> &amp;  <a href="yellow_6.html#K1" title="YELLOW_6:func.1">the_value_of</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="ref" href="yellow_6.html#T2" title="YELLOW_6:th.2">YELLOW_6:2</a></i>;<br/>


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