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<span class="kw">let </span><font color="Maroon" title="c1">ap</font>, <font color="Maroon" title="c2">bm</font>, <font color="Maroon" title="c3">cp</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="firebrick">::  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> <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#K8" title="FTACELL1:func.8">BitFTA1Circ</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dm</font>,<font color="Olive" title="b1">cin</font>)</span>)</span><br/>  for <font color="Olive" title="b3">a123x</font>, <font color="Olive" title="b4">a123y</font>, <font color="Olive" title="b5">a123z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>   st <font color="Olive" title="b3">a123x</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> <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>)</span>)</span>,<font color="Olive" title="b1">cin</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b4">a123y</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> <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="Olive" title="b1">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="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b5">a123z</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> <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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> holds <br/><span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Olive" title="b2">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K33" title="GFACIRC1:func.33">GFA2CarryOutput</a> (<span class="p2">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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"><font color="Olive" title="b3">a123x</font> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Olive" title="b4">a123y</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Olive" title="b5">a123z</font></span>)</span></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="firebrick">::  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#K8" title="FTACELL1:func.8">BitFTA1Circ</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font>)</span>)</span><br/>  for <font color="Olive" title="b2">a123x</font>, <font color="Olive" title="b3">a123y</font>, <font color="Olive" title="b4">a123z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>   st <font color="Olive" title="b2">a123x</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> <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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#K3" title="TWOSCOMP:func.3">and2a</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">a123y</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> <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="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b4">a123z</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> <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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> holds <br/><span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K33" title="GFACIRC1:func.33">GFA2CarryOutput</a> (<span class="p2">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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"><font color="Olive" title="b2">a123x</font> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Olive" title="b3">a123y</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Olive" title="b4">a123z</font></span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c6">S</font> =  <a href="ftacell1.html#K7" title="FTACELL1:func.7">BitFTA1Str</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c7">C</font> =  <a href="ftacell1.html#K8" title="FTACELL1:func.8">BitFTA1Circ</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c8">A1</font> =  <a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c9">A2</font> =  <a href="gfacirc1.html#K33" title="GFACIRC1:func.33">GFA2CarryOutput</a> (<span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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="c10">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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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#K3" title="TWOSCOMP:func.3">and2a</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">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="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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="c13">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#K8" title="FTACELL1:func.8">BitFTA1Circ</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a123x</font>, <font color="Olive" title="b2">a123y</font>, <font color="Olive" title="b3">a123z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>   st <font color="Olive" title="b1">a123x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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#K3" title="TWOSCOMP:func.3">and2a</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b2">a123y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <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="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">a123z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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> holds <br/><span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c13">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K33" title="GFACIRC1:func.33">GFA2CarryOutput</a> (<span class="p2">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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"><font color="Olive" title="b1">a123x</font> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Olive" title="b2">a123y</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Olive" title="b3">a123z</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c14">a123x</font>, <font color="Maroon" title="c15">a123y</font>, <font color="Maroon" title="c16">a123z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c14">a123x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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#K3" title="TWOSCOMP:func.3">and2a</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c15">a123y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <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="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c16">a123z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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> implies <span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c13">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K33" title="GFACIRC1:func.33">GFA2CarryOutput</a> (<span class="p2">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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"><font color="Maroon" title="c14">a123x</font> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Maroon" title="c15">a123y</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Maroon" title="c16">a123z</font></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:40"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
( <font color="Maroon" title="c14">a123x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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#K3" title="TWOSCOMP:func.3">and2a</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c15">a123y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <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="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c16">a123z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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 class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c13">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K33" title="GFACIRC1:func.33">GFA2CarryOutput</a> (<span class="p2">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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"><font color="Maroon" title="c14">a123x</font> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Maroon" title="c15">a123y</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Maroon" title="c16">a123z</font></span>)</span></span><br/>

<a NAME="E2:40"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
( <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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#K3" title="TWOSCOMP:func.3">and2a</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ftacell1.html#K7" title="FTACELL1:func.7">BitFTA1Str</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font>)</span>)</span> &amp; <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="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ftacell1.html#K7" title="FTACELL1:func.7">BitFTA1Str</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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="ref" href="ftacell1.html#T14" target="_self" title="FTACELL1:th.14">Th14</a></span>;<br/>
<a NAME="E3:40"/><span class="lab"><font color="Green" title="E32">A3</font></span>: 
( <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#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ftacell1.html#K7" title="FTACELL1:func.7">BitFTA1Str</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font>)</span>)</span> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c13">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ftacell1.html#K7" title="FTACELL1:func.7">BitFTA1Str</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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="ref" href="ftacell1.html#T14" target="_self" title="FTACELL1:th.14">Th14</a>, <a class="ref" href="circuit1.html#T3" title="CIRCUIT1:th.3">CIRCUIT1:3</a></span>;<br/>
<a NAME="E4:40"/>
 <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K7" title="FTACELL1:func.7">BitFTA1Str</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>,<font color="Maroon" title="c4">dm</font>,<font color="Maroon" title="c5">cin</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="ftacell1.html#K7" title="FTACELL1:func.7">BitFTA1Str</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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="ref" href="facirc_1.html#T37" title="FACIRC_1:th.37">FACIRC_1:37</a></span>;<br/>
<a NAME="E5:40"/><span class="kw">then </span>
 <a href="gfacirc1.html#K33" title="GFACIRC1:func.33">GFA2CarryOutput</a> (<span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>)</span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="ftacell1.html#K7" title="FTACELL1:func.7">BitFTA1Str</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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="ref" href="ftacell1.html#T15" target="_self" title="FTACELL1:th.15">Th15</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c13">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K33" title="GFACIRC1:func.33">GFA2CarryOutput</a> (<span class="p2">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>)</span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dm</font>)</span>)</span> = 
<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</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="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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#K3" title="TWOSCOMP:func.3">and2a</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="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="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</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="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">dm</font>,<span class="p5">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</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></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T35" title="FACIRC_1:th.35">FACIRC_1:35</a></span>
<br/>.= 
<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c14">a123x</font>,<font color="Maroon" title="c15">a123y</font>,<font color="Maroon" title="c16">a123z</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="txt" href="#E2:40"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="txt" href="#E3:40"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="ref" href="finseq_2.html#T126" title="FINSEQ_2:th.126">FINSEQ_2:126</a></span>
<br/>.= 
 <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a123x</font> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Maroon" title="c15">a123y</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Maroon" title="c16">a123z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="twoscomp.html#D28" title="TWOSCOMP:def.28">TWOSCOMP:def 28</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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