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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">c</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="facirc_2.html#NK3" title="FACIRC_2:NK.3">&lt;*&gt;</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( 1 <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> (<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<a href="facirc_2.html#NK3" title="FACIRC_2:NK.3">&lt;*&gt;</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a></span>)</span>)</span>)</span> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font>)</span>)</span> &amp; 1 <a href="gfacirc2.html#K6" title="GFACIRC2:func.6">-BitGFA1Circ</a> (<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> (<a href="facirc_2.html#NK3" title="FACIRC_2:NK.3">&lt;*&gt;</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a></span>)</span>)</span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K26" title="GFACIRC1:func.26">BitGFA1Circ</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font>)</span>)</span> &amp; 1 <a href="gfacirc2.html#K7" title="GFACIRC2:func.7">-BitGFA1CarryOutput</a> (<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font>) )</span><br/>

<a NAME="E1:28"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font>
 
;<br/>
<a NAME="E2:28"/>
<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:28"/>
 for <font color="Olive" title="b1">c</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="facirc_2.html#NK3" title="FACIRC_2:NK.3">&lt;*&gt;</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( 1 <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> (<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<a href="facirc_2.html#NK3" title="FACIRC_2:NK.3">&lt;*&gt;</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a></span>)</span>)</span>)</span> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font>)</span>)</span> &amp; 1 <a href="gfacirc2.html#K6" title="GFACIRC2:func.6">-BitGFA1Circ</a> (<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> (<a href="facirc_2.html#NK3" title="FACIRC_2:NK.3">&lt;*&gt;</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a></span>)</span>)</span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K26" title="GFACIRC1:func.26">BitGFA1Circ</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font>)</span>)</span> &amp; 1 <a href="gfacirc2.html#K7" title="GFACIRC2:func.7">-BitGFA1CarryOutput</a> (<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="gfacirc2.html#T17" target="_self" onmouseover="rs('gfacirc2/T17')" onmouseout="rh()">Th17</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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