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<span class="kw">let </span><font color="Maroon" title="c1">am</font>, <font color="Maroon" title="c2">bp</font>, <font color="Maroon" title="c3">cm</font>, <font color="Maroon" title="c4">dp</font> be  non  <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><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> <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#K14" title="FTACELL1:func.14">BitFTA2Circ</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</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#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">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#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</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="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">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">dp</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="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">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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#K2" title="TWOSCOMP:func.2">and2</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#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Olive" title="b1">cin</font>,<font color="Maroon" title="c4">dp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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><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"> 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#K14" title="FTACELL1:func.14">BitFTA2Circ</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</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#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">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#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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="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">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">dp</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">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">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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#K2" title="TWOSCOMP:func.2">and2</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#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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><br/>



<span class="kw">set </span><font color="Maroon" title="c6">S</font> =  <a href="ftacell1.html#K13" title="FTACELL1:func.13">BitFTA2Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</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#K14" title="FTACELL1:func.14">BitFTA2Circ</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</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#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">A2</font> =  <a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</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#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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="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="c11">cindp</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">dp</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="c12">dpA1</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">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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#K2" title="TWOSCOMP:func.2">and2</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#K14" title="FTACELL1:func.14">BitFTA2Circ</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</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">a123x</font>, <font color="Olive" title="b2">a123y</font>, <font color="Olive" title="b3">a123z</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">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#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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="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="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">dp</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">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">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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#K2" title="TWOSCOMP:func.2">and2</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#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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><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#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="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#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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="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="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">dp</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="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">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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#K2" title="TWOSCOMP:func.2">and2</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#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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><br/>



<span class="kw">assume </span><a NAME="E1:62"/><span class="lab"><font color="Green" title="E46">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#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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="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="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">dp</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="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">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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#K2" title="TWOSCOMP:func.2">and2</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="Red">::  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#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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><br/>

<a NAME="E2:62"/><span class="lab"><font color="Green" title="E47">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#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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="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#K13" title="FTACELL1:func.13">BitFTA2Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</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">dp</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#K13" title="FTACELL1:func.13">BitFTA2Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ftacell1.html#T24" target="_self" title="FTACELL1:th.24">Th24</a></span>;<br/>
<a NAME="E3:62"/><span class="lab"><font color="Green" title="E48">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">dp</font>,<span class="p3">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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#K2" title="TWOSCOMP:func.2">and2</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#K13" title="FTACELL1:func.13">BitFTA2Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</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#K13" title="FTACELL1:func.13">BitFTA2Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ftacell1.html#T24" target="_self" title="FTACELL1:th.24">Th24</a>, <a class="ref" href="circuit1.html#T4" title="CIRCUIT1:th.4">CIRCUIT1:4</a></span>;<br/>
<a NAME="E4:62"/>
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K13" title="FTACELL1:func.13">BitFTA2Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 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#K13" title="FTACELL1:func.13">BitFTA2Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</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="E5:62"/><span class="kw">then </span>
 <a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</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#K13" title="FTACELL1:func.13">BitFTA2Str</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font>,<font color="Maroon" title="c4">dp</font>,<font color="Maroon" title="c5">cin</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ftacell1.html#T25" target="_self" title="FTACELL1:th.25">Th25</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#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</font>,<font color="Maroon" title="c3">cm</font></span>)</span>,<font color="Maroon" title="c5">cin</font>,<font color="Maroon" title="c4">dp</font></span>)</span> = 
<a href="twoscomp.html#K25" title="TWOSCOMP:func.25">or3</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#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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="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="c5">cin</font>,<font color="Maroon" title="c4">dp</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="c4">dp</font>,<span class="p5">(<span class="default"><a href="gfacirc1.html#K36" title="GFACIRC1:func.36">GFA2AdderOutput</a> <font color="Maroon" title="c1">am</font>,<font color="Maroon" title="c2">bp</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#K2" title="TWOSCOMP:func.2">and2</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#K25" title="TWOSCOMP:func.25">or3</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="#E1:62"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="finseq_2.html#T146" title="FINSEQ_2:th.146">FINSEQ_2:146</a></span>
<br/>.= 
<span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="ref" href="twoscomp.html#D24" title="TWOSCOMP:def.24">TWOSCOMP:def 24</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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