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<span class="kw">let </span><font color="Maroon" title="c1">am</font>, <font color="Maroon" title="c2">bm</font>, <font color="Maroon" title="c3">cm</font>, <font color="Maroon" title="c4">dm</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">dm</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</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#K49" title="GFACIRC1:func.49">BitGFA3Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span> holds <br/>for <font color="Olive" title="b2">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="ftacell1.html#K20" title="FTACELL1:func.20">BitFTA3Circ</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Olive" title="b1">cin</font></span>)</span><br/> for <font color="Olive" title="b3">a1</font>, <font color="Olive" title="b4">a2</font>, <font color="Olive" title="b5">a3</font>, <font color="Olive" title="b6">a4</font>, <font color="Olive" title="b7">a5</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a>   st <font color="Olive" title="b3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> &amp; <font color="Olive" title="b4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> &amp; <font color="Olive" title="b5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> &amp; <font color="Olive" title="b6">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> &amp; <font color="Olive" title="b7">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">cin</font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b2">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K45" title="GFACIRC1:func.45">GFA3CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Olive" title="b1">cin</font>,<font color="Maroon" title="c4">dm</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b3">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b4">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b5">a3</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b7">a5</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b7">a5</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b6">a4</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b6">a4</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b3">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b4">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b5">a3</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b2">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a1</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b2">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b2">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b2">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">a4</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b2">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">cin</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">a5</font> )</span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">dm</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</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#K49" title="GFACIRC1:func.49">BitGFA3Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span> implies for <font color="Olive" title="b1">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="ftacell1.html#K20" title="FTACELL1:func.20">BitFTA3Circ</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font></span>)</span><br/> for <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</font>, <font color="Olive" title="b5">a4</font>, <font color="Olive" title="b6">a5</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a>   st <font color="Olive" title="b2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> &amp; <font color="Olive" title="b3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> &amp; <font color="Olive" title="b4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> &amp; <font color="Olive" title="b5">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> &amp; <font color="Olive" title="b6">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K45" title="GFACIRC1:func.45">GFA3CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b2">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b3">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b4">a3</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b6">a5</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b6">a5</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b5">a4</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b5">a4</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b2">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b3">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b4">a3</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a1</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a4</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">a5</font> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:86"/><span class="lab"><font color="Green" title="E64">A1</font></span>: 
( <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="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">dm</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</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#K49" title="GFACIRC1:func.49">BitGFA3Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="ftacell1.html#K20" title="FTACELL1:func.20">BitFTA3Circ</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font></span>)</span><br/> for <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</font>, <font color="Olive" title="b5">a4</font>, <font color="Olive" title="b6">a5</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a>   st <font color="Olive" title="b2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> &amp; <font color="Olive" title="b3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> &amp; <font color="Olive" title="b4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> &amp; <font color="Olive" title="b5">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> &amp; <font color="Olive" title="b6">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K45" title="GFACIRC1:func.45">GFA3CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b2">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b3">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b4">a3</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b6">a5</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b6">a5</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b5">a4</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b5">a4</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b2">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b3">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b4">a3</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a1</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a4</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">a5</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">S</font> =  <a href="ftacell1.html#K19" title="FTACELL1:func.19">BitFTA3Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font>;<br/>
<a NAME="E2:86"/><span class="lab"><font color="Green" title="E65">A2</font></span>: 
( <font color="Maroon" title="c1">am</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K19" title="FTACELL1:func.19">BitFTA3Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font></span>)</span> &amp; <font color="Maroon" title="c2">bm</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K19" title="FTACELL1:func.19">BitFTA3Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="ftacell1.html#T36" target="_self" title="FTACELL1:th.36">Th36</a></span>;<br/>
<a NAME="E3:86"/><span class="lab"><font color="Green" title="E66">A3</font></span>: 
( <font color="Maroon" title="c3">cm</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K19" title="FTACELL1:func.19">BitFTA3Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font></span>)</span> &amp; <font color="Maroon" title="c4">dm</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K19" title="FTACELL1:func.19">BitFTA3Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="ftacell1.html#T36" target="_self" title="FTACELL1:th.36">Th36</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">A1</font> =  <a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c8">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="ftacell1.html#K20" title="FTACELL1:func.20">BitFTA3Circ</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font>, <font color="Olive" title="b4">a4</font>, <font color="Olive" title="b5">a5</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a>   st <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> &amp; <font color="Olive" title="b2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> &amp; <font color="Olive" title="b3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> &amp; <font color="Olive" title="b4">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> &amp; <font color="Olive" title="b5">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K45" title="GFACIRC1:func.45">GFA3CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b1">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b2">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b3">a3</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b5">a5</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b5">a5</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b4">a4</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b4">a4</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b1">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b2">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b3">a3</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a1</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a4</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a5</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c9">dmA1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">dm</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c10">a1</font>, <font color="Maroon" title="c11">a2</font>, <font color="Maroon" title="c12">a3</font>, <font color="Maroon" title="c13">a4</font>, <font color="Maroon" title="c14">a5</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> &amp; <font color="Maroon" title="c11">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> &amp; <font color="Maroon" title="c12">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> &amp; <font color="Maroon" title="c13">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> &amp; <font color="Maroon" title="c14">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> implies ( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K45" title="GFACIRC1:func.45">GFA3CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c10">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c11">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c12">a3</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a5</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a5</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c13">a4</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c13">a4</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c10">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c11">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c12">a3</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a1</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a4</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a5</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E4:86"/><span class="lab"><font color="Green" title="E67">A4</font></span>: 
( <font color="Maroon" title="c10">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> &amp; <font color="Maroon" title="c11">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> &amp; <font color="Maroon" title="c12">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> &amp; <font color="Maroon" title="c13">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> &amp; <font color="Maroon" title="c14">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K45" title="GFACIRC1:func.45">GFA3CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c10">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c11">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c12">a3</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a5</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a5</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c13">a4</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c13">a4</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c10">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c11">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c12">a3</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a1</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a4</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a5</font> )</span><br/>

<a NAME="E5:86"/><span class="lab"><font color="Green" title="E68">A5</font></span>: 
<span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">dm</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c13">a4</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c10">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c11">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c12">a3</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E67">A4</font></span></a>, <a class="txt" href="ftacell1.html#E97"><span class="lab"><font color="Green" title="E59">Lm35</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">cindm</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">A1cin</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">A2</font> =  <a href="gfacirc1.html#K45" title="GFACIRC1:func.45">GFA3CarryOutput</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font>;<br/>
<a NAME="E6:86"/><span class="lab"><font color="Green" title="E69">A6</font></span>: 
 <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,<span class="p1">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T12" title="FACIRC_1:th.12">FACIRC_1:12</a></span>;<br/>
<a NAME="E7:86"/>
( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c10">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c11">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c12">a3</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a5</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a5</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c13">a4</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E67">A4</font></span></a>, <a class="txt" href="ftacell1.html#E97"><span class="lab"><font color="Green" title="E59">Lm35</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:86"/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K45" title="GFACIRC1:func.45">GFA3CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c10">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c11">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c12">a3</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a5</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a5</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c13">a4</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c13">a4</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c10">a1</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c11">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c12">a3</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:86"><span class="lab"><font color="Green" title="E69">A6</font></span></a>, <a class="txt" href="#E5:86"><span class="lab"><font color="Green" title="E68">A5</font></span></a>, <a class="txt" href="ftacell1.html#E99"><span class="lab"><font color="Green" title="E61">Lm37</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a1</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a4</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a5</font> )</span><br/>

<a NAME="E9:86"/><span class="lab"><font color="Green" title="E70">A7</font></span>: 
( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a4</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E67">A4</font></span></a>, <a class="txt" href="ftacell1.html#E97"><span class="lab"><font color="Green" title="E59">Lm35</font></span></a></span>;<br/>
<a NAME="E10:86"/><span class="lab"><font color="Green" title="E71">A8</font></span>: 
<span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E67">A4</font></span></a>, <a class="txt" href="ftacell1.html#E97"><span class="lab"><font color="Green" title="E59">Lm35</font></span></a></span>;<br/>
<a NAME="E11:86"/><span class="lab"><font color="Green" title="E72">A9</font></span>: 
<font color="Maroon" title="c5">cin</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K19" title="FTACELL1:func.19">BitFTA3Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="ftacell1.html#T36" target="_self" title="FTACELL1:th.36">Th36</a></span>;<br/>
<a NAME="E12:86"/>
( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a1</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E67">A4</font></span></a>, <a class="txt" href="ftacell1.html#E97"><span class="lab"><font color="Green" title="E59">Lm35</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:86"/>
( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">am</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a1</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">dm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a4</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c8">s</font>,4</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">cin</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a5</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:86"><span class="lab"><font color="Green" title="E69">A6</font></span></a>, <a class="txt" href="#E2:86"><span class="lab"><font color="Green" title="E65">A2</font></span></a>, <a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E66">A3</font></span></a>, <a class="txt" href="#E11:86"><span class="lab"><font color="Green" title="E72">A9</font></span></a>, <a class="txt" href="#E9:86"><span class="lab"><font color="Green" title="E70">A7</font></span></a>, <a class="txt" href="#E10:86"><span class="lab"><font color="Green" title="E71">A8</font></span></a>, <a class="ref" href="circuit2.html#D5" title="CIRCUIT2:def.5">CIRCUIT2:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>

<span class="kw">set </span><font color="Maroon" title="c18">C2</font> =  <a href="gfacirc1.html#K50" title="GFACIRC1:func.50">BitGFA3Circ</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">S2</font> =  <a href="gfacirc1.html#K49" title="GFACIRC1:func.49">BitGFA3Str</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K48" title="GFACIRC1:func.48">GFA3AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">C1</font> =  <a href="gfacirc1.html#K50" title="GFACIRC1:func.50">BitGFA3Circ</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">S1</font> =  <a href="gfacirc1.html#K49" title="GFACIRC1:func.49">BitGFA3Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">C</font> =  <a href="ftacell1.html#K20" title="FTACELL1:func.20">BitFTA3Circ</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font>;<br/>

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