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<b>let </b><font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c2">x2</font>, <font color="Maroon" title="c3">x3</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c4">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="c5">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of 3 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c4">X</font>;<br/><b>let </b><font color="Maroon" title="c6">S</font> be  <a href="circcmb3.html#V6" title="CIRCCMB3:attr.6">with_nonpair_inputs</a>  <a href="circcmb3.html#M1" title="CIRCCMB3:mode.1">Signature</a> of <font color="Maroon" title="c4">X</font>;<br/>







<b>assume </b><a NAME="E1:121"/><i><font color="Green" title="E58">A1</font></i>: 
( ( <font color="Maroon" title="c1">x1</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 <font color="Maroon" title="c6">S</font> or  not <font color="Maroon" title="c1">x1</font> is <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a> ) &amp; ( <font color="Maroon" title="c2">x2</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 <font color="Maroon" title="c6">S</font> or  not <font color="Maroon" title="c2">x2</font> is <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a> ) &amp; ( <font color="Maroon" title="c3">x3</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 <font color="Maroon" title="c6">S</font> or  not <font color="Maroon" title="c3">x3</font> is <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a> ) )
 ;<br/>

<a NAME="E2:121"/><i><font color="Green" title="E59">A2</font></i>: 
not  <a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c6">S</font>
 
<b>by </b><i><a class="ref" href="facirc_1.html#D2" title="FACIRC_1:def.2">FACIRC_1:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1"/>
( ( <font color="Maroon" title="c1">x1</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 <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c2">x2</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 <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c3">x3</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 <font color="Maroon" title="c6">S</font> ) or ( <font color="Maroon" title="c1">x1</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 <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c3">x3</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 <font color="Maroon" title="c6">S</font> ) or ( <font color="Maroon" title="c2">x2</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 <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c3">x3</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 <font color="Maroon" title="c6">S</font> ) or ( <font color="Maroon" title="c1">x1</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 <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c2">x2</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 <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> ) or ( <font color="Maroon" title="c1">x1</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 <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> ) or ( <font color="Maroon" title="c2">x2</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 <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> ) or ( not <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c3">x3</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 <font color="Maroon" title="c6">S</font> ) or ( not <font color="Maroon" title="c1">x1</font> is <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a> &amp; not <font color="Maroon" title="c2">x2</font> is <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a> &amp; not <font color="Maroon" title="c3">x3</font> is <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a> ) )
 </span><b>by </b><i><a class="txt" href="circcmb3.html#E1:121"><i><font color="Green" title="E58">A1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1"><b>suppose </b></a><a NAME="E1:121_1_1"/>
( ( <font color="Maroon" title="c1">x1</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 <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c2">x2</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 <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c3">x3</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 <font color="Maroon" title="c6">S</font> ) or ( <font color="Maroon" title="c1">x1</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 <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c3">x3</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 <font color="Maroon" title="c6">S</font> ) or ( <font color="Maroon" title="c2">x2</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 <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c3">x3</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 <font color="Maroon" title="c6">S</font> ) or ( <font color="Maroon" title="c1">x1</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 <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c2">x2</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 <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> ) or ( <font color="Maroon" title="c1">x1</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 <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> ) or ( <font color="Maroon" title="c2">x2</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 <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> ) or ( not <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; not <font color="Maroon" title="c2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> &amp; <font color="Maroon" title="c3">x3</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 <font color="Maroon" title="c6">S</font> ) )
 ;<br/><div class="add"><a NAME="E2:121_1_1"/><b>then </b>
(  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c6">S</font> or ( not <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a> &amp;  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c6">S</font></span>)</span> ) or ( not <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a> &amp;  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c6">S</font></span>)</span> ) or ( not <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x3</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a> &amp;  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x3</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c6">S</font></span>)</span> ) or ( not <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a> &amp;  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c6">S</font></span>)</span> ) or ( not <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a> &amp;  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c6">S</font></span>)</span> ) or ( not <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c3">x3</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a> &amp;  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c3">x3</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c6">S</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="circcmb3.html#E1:121"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="circcmb3.html#E2:121"><i><font color="Green" title="E59">A2</font></i></a>, <a class="txt" href="circcmb3.html#E67"><i><font color="Green" title="E53">Lm1</font></i></a>, <a class="txt" href="circcmb3.html#E70"><i><font color="Green" title="E56">Lm3</font></i></a>, <a class="ref" href="circcmb3.html#T45" target="_self" title="CIRCCMB3:th.45">Th45</a>, <a class="ref" href="circcmb3.html#T46" target="_self" title="CIRCCMB3:th.46">Th46</a>, <a class="ref" href="circcmb3.html#T47" target="_self" title="CIRCCMB3:th.47">Th47</a>, <a class="ref" href="circcmb3.html#T48" target="_self" title="CIRCCMB3:th.48">Th48</a>, <a class="ref" href="circcmb3.html#T49" target="_self" title="CIRCCMB3:th.49">Th49</a>, <a class="ref" href="circcmb3.html#T50" target="_self" title="CIRCCMB3:th.50">Th50</a>, <a class="ref" href="circcmb3.html#T51" target="_self" title="CIRCCMB3:th.51">Th51</a></i>;<br/><b>hence </b><a NAME="E3:121_1_1"/>
not  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> is <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a>
 <b>by </b><i><a class="txt" href="circcmb3.html#E68"><i><font color="Green" title="E54">Lm2</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="circcmb3.html#D11" target="_self" title="CIRCCMB3:def.11">CIRCCMB3:def 11</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_2"><b>suppose </b></a><a NAME="E1:121_1_2"/>
( not <font color="Maroon" title="c1">x1</font> is <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a> &amp; not <font color="Maroon" title="c2">x2</font> is <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a> &amp; not <font color="Maroon" title="c3">x3</font> is <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a> )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c8">b</font> = <font color="Maroon" title="c2">x2</font>, <font color="Maroon" title="c9">c</font> = <font color="Maroon" title="c3">x3</font> as  non <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/><a NAME="E3:121_1_2"/>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c9">c</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> &amp; <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c9">c</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c9">c</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">S</font> &amp; <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c9">c</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c6">S</font> )
 <b>by </b><i><a class="ref" href="facirc_1.html#T5" title="FACIRC_1:th.5">FACIRC_1:5</a>, <a class="ref" href="finseq_2.html#T148" title="FINSEQ_2:th.148">FINSEQ_2:148</a>, <a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/><a NAME="E4:121_1_2"/><b>then </b>
 <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c6">S</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c9">c</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="circcmb3.html#E2:121"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="circcmb3.html#T40" target="_self" title="CIRCCMB3:th.40">Th40</a></i>;<br/><b>hence </b><a NAME="E5:121_1_2"/>
not  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> is <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circcmb3.html#D11" target="_self" title="CIRCCMB3:def.11">CIRCCMB3:def 11</a><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
