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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> 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">dm</font>, <font color="Olive" title="b2">cin</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b3">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="Olive" title="b1">dm</font>,<font color="Olive" title="b2">cin</font></span>)</span><br/> for <font color="Olive" title="b4">a1</font>, <font color="Olive" title="b5">a2</font>, <font color="Olive" title="b6">a3</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="b4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">ap</font> &amp; <font color="Olive" title="b5">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">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="b6">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cp</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="b3">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K9" title="FTACELL1:func.9">BitFTA1CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>,<font color="Olive" title="b1">dm</font>,<font color="Olive" title="b2">cin</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b5">a2</font></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">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b6">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b4">a1</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="Olive" title="b3">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K10" title="FTACELL1:func.10">BitFTA1AdderOutputI</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font>,<font color="Olive" title="b1">dm</font>,<font color="Olive" title="b2">cin</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="b4">a1</font> <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="Olive" title="b5">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Olive" title="b6">a3</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">dm</font>, <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#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">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</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">ap</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">cp</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>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K9" title="FTACELL1:func.9">BitFTA1CarryOutput</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<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#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="b3">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b4">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b2">a1</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="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K10" title="FTACELL1:func.10">BitFTA1AdderOutputI</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>  <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">a1</font> <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="Olive" title="b3">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Olive" title="b4">a3</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">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="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> 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="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">ap</font> &amp; <font color="Olive" title="b2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">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="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cp</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="c6">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K9" title="FTACELL1:func.9">BitFTA1CarryOutput</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<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#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="b2">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b3">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b1">a1</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="c6">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K10" title="FTACELL1:func.10">BitFTA1AdderOutputI</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>  <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">a1</font> <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="Olive" title="b2">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Olive" title="b3">a3</font></span>)</span> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c7">S1</font> =  <a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</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="c8">C1</font> =  <a href="gfacirc1.html#K26" title="GFACIRC1:func.26">BitGFA1Circ</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">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="c10">A2</font> =  <a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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="c11">S2</font> =  <a href="gfacirc1.html#K37" title="GFACIRC1:func.37">BitGFA2Str</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="c12">C2</font> =  <a href="gfacirc1.html#K38" title="GFACIRC1:func.38">BitGFA2Circ</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">let </span><font color="Maroon" title="c13">a1</font>, <font color="Maroon" title="c14">a2</font>, <font color="Maroon" title="c15">a3</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="c13">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">ap</font> &amp; <font color="Maroon" title="c14">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">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="c15">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cp</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="c6">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K9" title="FTACELL1:func.9">BitFTA1CarryOutput</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a2</font></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="c14">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c15">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c13">a1</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="c6">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K10" title="FTACELL1:func.10">BitFTA1AdderOutputI</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>  <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="c13">a1</font> <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="c14">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c15">a3</font></span>)</span> ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:34"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c13">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">ap</font>
 <span class="kw">and </span><br/><a NAME="E2:34"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<font color="Maroon" title="c14">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font>
 <span class="kw">and </span><br/><a NAME="E3:34"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<font color="Maroon" title="c15">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cp</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="c6">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K9" title="FTACELL1:func.9">BitFTA1CarryOutput</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a2</font></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="c14">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c15">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c13">a1</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="c6">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K10" title="FTACELL1:func.10">BitFTA1AdderOutputI</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>  <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="c13">a1</font> <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="c14">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c15">a3</font></span>)</span> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c16">s1</font> = <font color="Maroon" title="c6">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font></span>)</span> as   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K26" title="GFACIRC1:func.26">BitGFA1Circ</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 class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T26" title="FACIRC_1:th.26">FACIRC_1:26</a></span>;<br/>
<a NAME="E5:34"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c16">s1</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="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</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 class="kw">by</span> <span class="lab"><a class="ref" href="circuit1.html#T4" title="CIRCUIT1:th.4">CIRCUIT1:4</a></span>;<br/>
<a NAME="E6:34"/>
<font color="Maroon" title="c1">ap</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</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 class="kw">by</span> <span class="lab"><a class="ref" href="gfacirc1.html#T81" title="GFACIRC1:th.81">GFACIRC1:81</a></span>;<br/>
<a NAME="E7:34"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A5</font></span>: 
<font color="Maroon" title="c13">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">ap</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E5:34"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">t</font> = <font color="Maroon" title="c6">s</font> as   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K26" title="GFACIRC1:func.26">BitGFA1Circ</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K38" title="GFACIRC1:func.38">BitGFA2Circ</a> <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>,<font color="Maroon" title="c4">dm</font></span>)</span></span>)</span> ;<br/>
<a NAME="E9:34"/><span class="lab"><font color="Green" title="E29">A6</font></span>: 
 <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K37" title="GFACIRC1:func.37">BitGFA2Str</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="ftacell1.html#E32"><span class="lab"><font color="Green" title="E19">Lm12</font></span></a></span>;<br/>
<a NAME="E10:34"/>
<font color="Maroon" title="c3">cp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</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 class="kw">by</span> <span class="lab"><a class="ref" href="gfacirc1.html#T81" title="GFACIRC1:th.81">GFACIRC1:81</a></span>;<br/>
<a NAME="E11:34"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A7</font></span>: 
<font color="Maroon" title="c15">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">cp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E5:34"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>;<br/>
<a NAME="E12:34"/>
<font color="Maroon" title="c2">bm</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</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 class="kw">by</span> <span class="lab"><a class="ref" href="gfacirc1.html#T81" title="GFACIRC1:th.81">GFACIRC1:81</a></span>;<br/>
<a NAME="E13:34"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A8</font></span>: 
<font color="Maroon" title="c14">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">bm</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E5:34"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>;<br/>
<a NAME="E14:34"/>
 <a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</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 class="kw">by</span> <span class="lab"><a class="ref" href="gfacirc1.html#T81" title="GFACIRC1:th.81">GFACIRC1:81</a></span>;<br/>
<a NAME="E15:34"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c17">t</font>,2</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> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c16">s1</font>,2</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> <font color="Maroon" title="c1">ap</font>,<font color="Maroon" title="c2">bm</font>,<font color="Maroon" title="c3">cp</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:34"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="ref" href="facirc_1.html#T32" title="FACIRC_1:th.32">FACIRC_1:32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:34"/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c6">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K9" title="FTACELL1:func.9">BitFTA1CarryOutput</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c14">a2</font></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="c14">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c15">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c13">a1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:34"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E13:34"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E11:34"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="ref" href="gfacirc1.html#T84" title="GFACIRC1:th.84">GFACIRC1:84</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="c6">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K10" title="FTACELL1:func.10">BitFTA1AdderOutputI</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>  <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="c13">a1</font> <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="c14">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c15">a3</font></span>)</span></span><br/>

<a NAME="E17:34"/>
 <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> <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="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</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 class="kw">by</span> <span class="lab"><a class="ref" href="gfacirc1.html#T81" title="GFACIRC1:th.81">GFACIRC1:81</a></span>;<br/>
<a NAME="E18:34"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c17">t</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c16">s1</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:34"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="ref" href="facirc_1.html#T32" title="FACIRC_1:th.32">FACIRC_1:32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:34"/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c6">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ftacell1.html#K10" title="FTACELL1:func.10">BitFTA1AdderOutputI</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>  <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="c13">a1</font> <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="c14">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c15">a3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:34"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E13:34"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E11:34"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="ref" href="gfacirc1.html#T84" title="GFACIRC1:th.84">GFACIRC1:84</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/>


</div>
