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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">z</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"> ( <font color="Maroon" title="c1">x</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#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span> &amp; <font color="Maroon" title="c2">y</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#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span> &amp; <font color="Maroon" title="c3">z</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#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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="c1">x</font>,<font color="Maroon" title="c2">y</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="gfacirc1.html#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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="c2">y</font>,<font color="Maroon" title="c3">z</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="gfacirc1.html#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#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#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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#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"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="c2">y</font>,<font color="Maroon" title="c3">z</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</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="gfacirc1.html#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">f1</font> =  <a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">f2</font> =  <a href="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">f3</font> =  <a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">f4</font> =  <a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">xy</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="c1">x</font>,<font color="Maroon" title="c2">y</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="c9">yz</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="c2">y</font>,<font color="Maroon" title="c3">z</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="c10">zx</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">xyz</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#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"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="c2">y</font>,<font color="Maroon" title="c3">z</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">Cxy</font> =  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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>);<br/>
<span class="kw">set </span><font color="Maroon" title="c13">Cyz</font> =  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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>);<br/>
<span class="kw">set </span><font color="Maroon" title="c14">Czx</font> =  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a>);<br/>
<span class="kw">set </span><font color="Maroon" title="c15">Cxyz</font> =  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</a>);<br/>
<span class="kw">set </span><font color="Maroon" title="c16">p</font> = <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>;<br/>
<a NAME="E1:114"/>
<font color="Maroon" title="c3">z</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="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T43" title="FACIRC_1:th.43">FACIRC_1:43</a></span>;<br/>
<a NAME="E2:114"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A1</font></span>: 
<font color="Maroon" title="c3">z</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#K29" title="GFACIRC1:func.29">GFA2CarryIStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></span>;<br/>
<a NAME="E3:114"/>
<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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#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="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T43" title="FACIRC_1:th.43">FACIRC_1:43</a></span>;<br/>
<a NAME="E4:114"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">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"><font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#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#K29" title="GFACIRC1:func.29">GFA2CarryIStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></span>;<br/>
<a NAME="E5:114"/>
<font color="Maroon" title="c2">y</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="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T43" title="FACIRC_1:th.43">FACIRC_1:43</a></span>;<br/>
<a NAME="E6:114"/><span class="kw">then </span>
<font color="Maroon" title="c2">y</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"><span class="p2">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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>)</span> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <span class="p2">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></span>;<br/>
<a NAME="E7:114"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A3</font></span>: 
<font color="Maroon" title="c2">y</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#K29" title="GFACIRC1:func.29">GFA2CarryIStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></span>;<br/>
<a NAME="E8:114"/>
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</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"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="c2">y</font>,<font color="Maroon" title="c3">z</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</a>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</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"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="c2">y</font>,<font color="Maroon" title="c3">z</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></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#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"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="c2">y</font>,<font color="Maroon" title="c3">z</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D6" title="CIRCCOMB:def.6">CIRCCOMB:def 6</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E9:114"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A4</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#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"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="c2">y</font>,<font color="Maroon" title="c3">z</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</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="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</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"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="c2">y</font>,<font color="Maroon" title="c3">z</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</a>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E10:114"/>
<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="c2">y</font>,<font color="Maroon" title="c3">z</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="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T43" title="FACIRC_1:th.43">FACIRC_1:43</a></span>;<br/>
<a NAME="E11:114"/><span class="kw">then </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="c2">y</font>,<font color="Maroon" title="c3">z</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"><span class="p2">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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>)</span> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <span class="p2">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></span>;<br/>
<a NAME="E12:114"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A5</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="c2">y</font>,<font color="Maroon" title="c3">z</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="gfacirc1.html#K29" title="GFACIRC1:func.29">GFA2CarryIStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></span>;<br/>
<a NAME="E13:114"/>
<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="c1">x</font>,<font color="Maroon" title="c2">y</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="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T43" title="FACIRC_1:th.43">FACIRC_1:43</a></span>;<br/>
<a NAME="E14:114"/><span class="kw">then </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="c1">x</font>,<font color="Maroon" title="c2">y</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"><span class="p2">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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>)</span> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <span class="p2">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></span>;<br/>
<a NAME="E15:114"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A6</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="c1">x</font>,<font color="Maroon" title="c2">y</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="gfacirc1.html#K29" title="GFACIRC1:func.29">GFA2CarryIStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></span>;<br/>
<a NAME="E16:114"/>
<font color="Maroon" title="c1">x</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="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T43" title="FACIRC_1:th.43">FACIRC_1:43</a></span>;<br/>
<a NAME="E17:114"/><span class="kw">then </span>
<font color="Maroon" title="c1">x</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#K29" title="GFACIRC1:func.29">GFA2CarryIStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:114"/>
( <font color="Maroon" title="c1">x</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#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span> &amp; <font color="Maroon" title="c2">y</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#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span> &amp; <font color="Maroon" title="c3">z</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#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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="c1">x</font>,<font color="Maroon" title="c2">y</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="gfacirc1.html#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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="c2">y</font>,<font color="Maroon" title="c3">z</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="gfacirc1.html#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#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#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</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#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"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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="c2">y</font>,<font color="Maroon" title="c3">z</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="c3">z</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="twoscomp.html#K29" title="TWOSCOMP:func.29">nor3</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="gfacirc1.html#K31" title="GFACIRC1:func.31">GFA2CarryStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font>)</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:114"><span class="lab"><font color="Green" title="E65">A3</font></span></a>, <a class="txt" href="#E2:114"><span class="lab"><font color="Green" title="E63">A1</font></span></a>, <a class="txt" href="#E15:114"><span class="lab"><font color="Green" title="E68">A6</font></span></a>, <a class="txt" href="#E12:114"><span class="lab"><font color="Green" title="E67">A5</font></span></a>, <a class="txt" href="#E4:114"><span class="lab"><font color="Green" title="E64">A2</font></span></a>, <a class="txt" href="#E9:114"><span class="lab"><font color="Green" title="E66">A4</font></span></a>, <a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
