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<b>let </b><font color="Maroon" title="c1">ap</font>, <font color="Maroon" title="c2">bp</font>, <font color="Maroon" title="c3">cp</font>, <font color="Maroon" title="c4">dp</font> be  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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">cin</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">cin</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c4">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; not <font color="Olive" title="b1">cin</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span> holds <br/> <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K1" title="FTACELL1:func.1">BitFTA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dp</font>,<font color="Olive" title="b1">cin</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dp</font>,<font color="Olive" title="b1">cin</font></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span></span><br/><b>let </b><font color="Maroon" title="c5">cin</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">cin</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c4">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; not <font color="Maroon" title="c5">cin</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span> implies  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K1" title="FTACELL1:func.1">BitFTA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> )</span><br/>



<b>set </b><font color="Maroon" title="c6">S</font> =  <a href="ftacell1.html#K1" title="FTACELL1:func.1">BitFTA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font>;<br/>
<b>set </b><font color="Maroon" title="c7">S1</font> =  <a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>;<br/>
<b>set </b><font color="Maroon" title="c8">A1</font> =  <a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>;<br/>
<b>set </b><font color="Maroon" title="c9">C1</font> =  <a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>;<br/>
<b>set </b><font color="Maroon" title="c10">S2</font> =  <a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font>;<br/>
<b>set </b><font color="Maroon" title="c11">A2</font> =  <a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font>;<br/>
<b>set </b><font color="Maroon" title="c12">C2</font> =  <a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font>;<br/>
<b>set </b><font color="Maroon" title="c13">apbp0</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c14">apbp</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c15">bpcp</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c16">cpap</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c17">A1cin0</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c18">A1cin</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c19">cindp</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c20">dpA1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c4">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>assume </b><a NAME="E1:7"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c5">cin</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c4">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; not <font color="Maroon" title="c5">cin</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K1" title="FTACELL1:func.1">BitFTA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span></span><br/>

<a NAME="E2:7"/><b>then </b><i><font color="Green" title="E6">A2</font></i>: 
( <font color="Maroon" title="c4">dp</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp;  <a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c5">cin</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c4">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c4">dp</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 
<b>by </b><i><a class="txt" href="ftacell1.html#E5"><i><font color="Green" title="E2">LemmaX11</font></i></a></i>;<br/>
<a NAME="E3:7"/><i><font color="Green" title="E7">A3</font></i>: 
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ftacell1.html#E6"><i><font color="Green" title="E3">LemmaX12</font></i></a></i>;<br/>
<i><font color="Green" title="E8">A4</font></i>:  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></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="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="gfacirc1.html#T39" title="GFACIRC1:th.39">GFACIRC1:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></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="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41" title="ENUMSET1:th.41">ENUMSET1:41</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></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"><span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></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"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T46" title="ENUMSET1:th.46">ENUMSET1:46</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T52" title="ENUMSET1:th.52">ENUMSET1:52</a></i>
;<br/>
<a NAME="E5:7"/>
 <a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/>
<a NAME="E6:7"/><b>then </b><i><font color="Green" title="E9">A5</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T68" title="ZFMISC_1:th.68">ZFMISC_1:68</a></i>;<br/>
<a NAME="E7:7"/><i><font color="Green" title="E10">A6</font></i>: 
not <font color="Maroon" title="c4">dp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/>
<i><font color="Green" title="E11">A7</font></i>: <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></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="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
<b>by </b><i><a class="txt" href="#E4:7"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="enumset1.html#T42" title="ENUMSET1:th.42">ENUMSET1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T42" title="XBOOLE_1:th.42">XBOOLE_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">cin</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="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">dp</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
<b>by </b><i><a class="txt" href="#E6:7"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="enumset1.html#T41" title="ENUMSET1:th.41">ENUMSET1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">cin</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">dp</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T42" title="XBOOLE_1:th.42">XBOOLE_1:42</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">cin</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"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">dp</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c1">ap</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K9" title="GFACIRC1:func.9">GFA0CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="#E4:7"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="zfmisc_1.html#T67" title="ZFMISC_1:th.67">ZFMISC_1:67</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">cin</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"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">dp</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="txt" href="#E7:7"><i><font color="Green" title="E10">A6</font></i></a>, <a class="ref" href="zfmisc_1.html#T67" title="ZFMISC_1:th.67">ZFMISC_1:67</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41" title="ENUMSET1:th.41">ENUMSET1:41</a></i>
;<br/>
<a NAME="E9:7"/>
(  <a href="ftacell1.html#K1" title="FTACELL1:func.1">BitFTA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span>)</span> &amp;  <a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a>  <a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font> )
 
<b>by </b><i><a class="ref" href="circcomb.html#T55" title="CIRCCOMB:th.55">CIRCCOMB:55</a></i>;<br/>
<b>hence </b> <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K1" title="FTACELL1:func.1">BitFTA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p3">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <span class="p4">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p3">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:7"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="facirc_1.html#T4" title="FACIRC_1:th.4">FACIRC_1:4</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p3">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <span class="p4">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p3">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#T42" title="GFACIRC1:th.42">GFACIRC1:42</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p3">(<span class="default"><a href="gfacirc1.html#K13" title="GFACIRC1:func.13">BitGFA0Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E2:7"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="gfacirc1.html#T41" title="GFACIRC1:th.41">GFACIRC1:41</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
<b>by </b><i><a class="txt" href="#E8:7"><i><font color="Green" title="E11">A7</font></i></a>, <a class="ref" href="enumset1.html#T49" title="ENUMSET1:th.49">ENUMSET1:49</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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