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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>] <span class="kw">means </span> for <font color="Olive" title="b1">z</font> being   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of $1, <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> <br/>  for <font color="Olive" title="b2">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>  holds   <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>;<br/>
<a NAME="E1:22"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[1]
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">z</font> be   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of 1, <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</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">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>  holds   <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</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">  <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">NZD</font> = <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">DPI</font> = <font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">NZ1</font> = <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">B1</font> = <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1;<br/>
<a NAME="E1:22_1"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T3" onmouseover="rs('finseq_1/T3')" onmouseout="rh()">FINSEQ_1:3</a></span>;<br/>
<span class="lab"><font color="Green" title="E18">A3</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span>,<span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></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"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D6" onmouseover="rs('binarith/D6')" onmouseout="rh()">BINARITH:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></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"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D2" onmouseover="rs('binarith/D2')" onmouseout="rh()">BINARITH:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></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"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D2" onmouseover="rs('binarith/D2')" onmouseout="rh()">BINARITH:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binari_2.html#T5" target="_self" onmouseover="rs('binari_2/T5')" onmouseout="rh()">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binarith.html#D1" onmouseover="rs('binarith/D1')" onmouseout="rh()">BINARITH:def 1</a></span>
;<br/>
<span class="lab"><font color="Green" title="E19">A4</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></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"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D6" onmouseover="rs('binarith/D6')" onmouseout="rh()">BINARITH:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></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"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D2" onmouseover="rs('binarith/D2')" onmouseout="rh()">BINARITH:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></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"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D2" onmouseover="rs('binarith/D2')" onmouseout="rh()">BINARITH:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binari_2.html#T5" target="_self" onmouseover="rs('binari_2/T5')" onmouseout="rh()">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binarith.html#D1" onmouseover="rs('binarith/D1')" onmouseout="rh()">BINARITH:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binarith.html#D5" onmouseover="rs('binarith/D5')" onmouseout="rh()">BINARITH:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D2" onmouseover="rs('binarith/D2')" onmouseout="rh()">BINARITH:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binari_2.html#T5" target="_self" onmouseover="rs('binari_2/T5')" onmouseout="rh()">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binarith.html#D1" onmouseover="rs('binarith/D1')" onmouseout="rh()">BINARITH:def 1</a></span>
;<br/>
<span class="lab"><font color="Green" title="E20">A5</font></span>:  <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T9" target="_self" onmouseover="rs('binari_2/T9')" onmouseout="rh()">Th9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T7" target="_self" onmouseover="rs('binari_2/T7')" onmouseout="rh()">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span>,<span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T19" onmouseover="rs('binarith/T19')" onmouseout="rh()">BINARITH:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="ref" href="binari_2.html#T9" target="_self" onmouseover="rs('binari_2/T9')" onmouseout="rh()">Th9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T7" target="_self" onmouseover="rs('binari_2/T7')" onmouseout="rh()">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="ref" href="binarith.html#T19" onmouseover="rs('binarith/T19')" onmouseout="rh()">BINARITH:19</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E21">A6</font></span>: <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binarith.html#T1" onmouseover="rs('binarith/T1')" onmouseout="rh()">BINARITH:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binarith.html#D5" onmouseover="rs('binarith/D5')" onmouseout="rh()">BINARITH:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D2" onmouseover="rs('binarith/D2')" onmouseout="rh()">BINARITH:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binari_2.html#T5" target="_self" onmouseover="rs('binari_2/T5')" onmouseout="rh()">Th5</a></span>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binarith.html#D1" onmouseover="rs('binarith/D1')" onmouseout="rh()">BINARITH:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binarith.html#D5" onmouseover="rs('binarith/D5')" onmouseout="rh()">BINARITH:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> 1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D2" onmouseover="rs('binarith/D2')" onmouseout="rh()">BINARITH:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binari_2.html#T5" target="_self" onmouseover="rs('binari_2/T5')" onmouseout="rh()">Th5</a></span>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="binarith.html#D1" onmouseover="rs('binarith/D1')" onmouseout="rh()">BINARITH:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1

;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">p</font> = <font color="Maroon" title="c2">d</font>, <font color="Maroon" title="c8">q</font> = <font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 as   <a href="xboolean.html#V1" title="XBOOLEAN:attr.1">boolean</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/>
<span class="lab"><font color="Green" title="E22">A7</font></span>: <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <font color="Maroon" title="c8">q</font></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <font color="Maroon" title="c8">q</font></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p3">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c8">q</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K10" title="XBOOLEAN:func.10">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T8" onmouseover="rs('xboolean/T8')" onmouseout="rh()">XBOOLEAN:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c7">p</font></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c8">q</font></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c8">q</font></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <font color="Maroon" title="c8">q</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K10" title="XBOOLEAN:func.10">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T8" onmouseover="rs('xboolean/T8')" onmouseout="rh()">XBOOLEAN:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></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"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T8" onmouseover="rs('xboolean/T8')" onmouseout="rh()">XBOOLEAN:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></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"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</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"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T8" onmouseover="rs('xboolean/T8')" onmouseout="rh()">XBOOLEAN:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</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"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T8" onmouseover="rs('xboolean/T8')" onmouseout="rh()">XBOOLEAN:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></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"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></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"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</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"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T8" onmouseover="rs('xboolean/T8')" onmouseout="rh()">XBOOLEAN:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</font></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"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</font></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"><span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c2">d</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>
<br/>.= 
<font color="Maroon" title="c2">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T8" onmouseover="rs('xboolean/T8')" onmouseout="rh()">XBOOLEAN:8</a></span>
<br/>.= 
<a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c2">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T102" onmouseover="rs('xboolean/T102')" onmouseout="rh()">XBOOLEAN:102</a></span>
<br/>.= 
<font color="Maroon" title="c2">d</font>

;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">k1</font>, <font color="Maroon" title="c10">k2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> <span class="kw"> such that </span><br/><a NAME="E9:22_1"/><span class="lab"><font color="Green" title="E23">A8</font></span>: 
 <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c9">k1</font>,<font color="Maroon" title="c10">k2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T100" onmouseover="rs('finseq_2/T100')" onmouseout="rh()">FINSEQ_2:100</a></span>;<br/>
<a NAME="E10:22_1"/><span class="lab"><font color="Green" title="E24">A9</font></span>: 
( <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">k1</font> &amp; <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">k2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:22_1"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="ref" href="finseq_4.html#T17" onmouseover="rs('finseq_4/T17')" onmouseout="rh()">FINSEQ_4:17</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> <span class="kw"> such that </span><br/><a NAME="E12:22_1"/><span class="lab"><font color="Green" title="E25">A10</font></span>: 
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c11">k</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T97" onmouseover="rs('finseq_2/T97')" onmouseout="rh()">FINSEQ_2:97</a></span>;<br/>
<a NAME="E13:22_1"/>
 <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c11">k</font>,<font color="Maroon" title="c2">d</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22_1"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E7:22_1"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E9:22_1"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="txt" href="#E10:22_1"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="#E12:22_1"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="ref" href="finseq_4.html#T16" onmouseover="rs('finseq_4/T16')" onmouseout="rh()">FINSEQ_4:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:22_1"/>
 <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:22_1"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="ref" href="finseq_1.html#D9" onmouseover="rs('finseq_1/D9')" onmouseout="rh()">FINSEQ_1:def 9</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/>


</div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E17">A11</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_2"><span class="kw">now </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">  for <font color="Olive" title="b1">m</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c1">m</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">m</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/><span class="kw">assume </span><a NAME="E1:22_2"/><span class="lab"><font color="Green" title="E18">A12</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">m</font>]
 ; <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"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_2_1"><span class="kw">now </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">  for <font color="Olive" title="b1">z</font> being   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1, <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> <br/>  for <font color="Olive" title="b2">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>  holds   <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">z</font> be   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1, <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</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">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>  holds   <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</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">  <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span><br/><span class="kw">consider </span><font color="Maroon" title="c4">t</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">m</font> <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>, <font color="Maroon" title="c5">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> <span class="kw"> such that </span><br/><a NAME="E2:22_2_1"/><span class="lab"><font color="Green" title="E19">A13</font></span>: 
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">k</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T117" onmouseover="rs('finseq_2/T117')" onmouseout="rh()">FINSEQ_2:117</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c6">A</font> =  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>);<br/><span class="kw">set </span><font color="Maroon" title="c7">B</font> =  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>);<br/> <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">k</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> = 
 <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T14" target="_self" onmouseover="rs('binari_2/T14')" onmouseout="rh()">Th14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T14" target="_self" onmouseover="rs('binari_2/T14')" onmouseout="rh()">Th14</a></span>
;<br/><a NAME="E4:22_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A14</font></span>: 
<span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">k</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>;<br/><a NAME="E5:22_2_1"/><span class="lab"><font color="Green" title="E21">A15</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">k</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c8">p</font> = <font color="Maroon" title="c5">k</font>, <font color="Maroon" title="c9">q</font> =  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>) as   <a href="xboolean.html#V1" title="XBOOLEAN:attr.1">boolean</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c8">p</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c9">q</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c8">p</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c9">q</font></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c9">q</font></span>)</span></span>)</span> <a href="xboolean.html#K10" title="XBOOLEAN:func.10">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T8" onmouseover="rs('xboolean/T8')" onmouseout="rh()">XBOOLEAN:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">k</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></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="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T11" onmouseover="rs('xboolean/T11')" onmouseout="rh()">XBOOLEAN:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T11" onmouseover="rs('xboolean/T11')" onmouseout="rh()">XBOOLEAN:11</a></span>
<br/>.= 
<font color="Maroon" title="c5">k</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T73" onmouseover="rs('xboolean/T73')" onmouseout="rh()">XBOOLEAN:73</a></span>
;<br/><a NAME="E8:22_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A16</font></span>: 
<font color="Maroon" title="c5">k</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_2"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E4:22_2_1"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E5:22_2_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a></span>;<br/><span class="lab"><font color="Green" title="E23">A17</font></span>: <font color="Maroon" title="c5">k</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">k</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">k</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T73" onmouseover="rs('xboolean/T73')" onmouseout="rh()">XBOOLEAN:73</a></span>
<br/>.= 
<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>

;<br/><a NAME="E10:22_2_1"/><span class="lab"><font color="Green" title="E24">A18</font></span>: 
<font color="Maroon" title="c5">k</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">k</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>;<br/><span class="lab"><font color="Green" title="E25">A19</font></span>: <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T73" onmouseover="rs('xboolean/T73')" onmouseout="rh()">XBOOLEAN:73</a></span>
<br/>.= 
<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>
<br/>.= 
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)

;<br/><a NAME="E12:22_2_1"/><span class="lab"><font color="Green" title="E26">A20</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T3" onmouseover="rs('finseq_1/T3')" onmouseout="rh()">FINSEQ_1:3</a></span>;<br/><span class="lab"><font color="Green" title="E27">A21</font></span>:  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c2">z</font></span>)</span>,<span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>) = 
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_2_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="ref" href="binari_2.html#T9" target="_self" onmouseover="rs('binari_2/T9')" onmouseout="rh()">Th9</a></span>
<br/>.= 
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T7" target="_self" onmouseover="rs('binari_2/T7')" onmouseout="rh()">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D6" onmouseover="rs('binarith/D6')" onmouseout="rh()">BINARITH:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T18" onmouseover="rs('binarith/T18')" onmouseout="rh()">BINARITH:18</a></span>
;<br/><span class="lab"><font color="Green" title="E28">A22</font></span>:  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>) = 
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T7" target="_self" onmouseover="rs('binari_2/T7')" onmouseout="rh()">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></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"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D6" onmouseover="rs('binarith/D6')" onmouseout="rh()">BINARITH:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></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"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">k</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_2_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="ref" href="binari_2.html#T9" target="_self" onmouseover="rs('binari_2/T9')" onmouseout="rh()">Th9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T9" target="_self" onmouseover="rs('binari_2/T9')" onmouseout="rh()">Th9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T7" target="_self" onmouseover="rs('binari_2/T7')" onmouseout="rh()">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T7" target="_self" onmouseover="rs('binari_2/T7')" onmouseout="rh()">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:22_2_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="ref" href="binarith.html#D1" onmouseover="rs('binarith/D1')" onmouseout="rh()">BINARITH:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:22_2_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="ref" href="binarith.html#D5" onmouseover="rs('binarith/D5')" onmouseout="rh()">BINARITH:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p0"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T18" onmouseover="rs('binarith/T18')" onmouseout="rh()">BINARITH:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T19" onmouseover="rs('binarith/T19')" onmouseout="rh()">BINARITH:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T9" target="_self" onmouseover="rs('binari_2/T9')" onmouseout="rh()">Th9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">k</font> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:22_2_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E9:22_2_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E10:22_2_1"><span class="lab"><font color="Green" title="E24">A18</font></span></a>, <a class="txt" href="#E11:22_2_1"><span class="lab"><font color="Green" title="E25">A19</font></span></a>, <a class="ref" href="binarith.html#T18" onmouseover="rs('binarith/T18')" onmouseout="rh()">BINARITH:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">k</font> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T6" onmouseover="rs('xboolean/T6')" onmouseout="rh()">XBOOLEAN:6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T11" onmouseover="rs('xboolean/T11')" onmouseout="rh()">XBOOLEAN:11</a></span>
;<br/><span class="kw">set </span><font color="Maroon" title="c10">C</font> = <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c11">p</font> = <font color="Maroon" title="c3">d</font>, <font color="Maroon" title="c12">q</font> = <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p2">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> as   <a href="xboolean.html#V1" title="XBOOLEAN:attr.1">boolean</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/><span class="lab"><font color="Green" title="E29">A23</font></span>: <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">p</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c11">p</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c12">q</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c11">p</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p4">(<span class="default"><a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <font color="Maroon" title="c12">q</font></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c12">q</font></span>)</span></span>)</span> <a href="xboolean.html#K10" title="XBOOLEAN:func.10">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T8" onmouseover="rs('xboolean/T8')" onmouseout="rh()">XBOOLEAN:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">d</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p5">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></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"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p4">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p0">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p1">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T11" onmouseover="rs('xboolean/T11')" onmouseout="rh()">XBOOLEAN:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p3">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T11" onmouseover="rs('xboolean/T11')" onmouseout="rh()">XBOOLEAN:11</a></span>
<br/>.= 
<font color="Maroon" title="c3">d</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T73" onmouseover="rs('xboolean/T73')" onmouseout="rh()">XBOOLEAN:73</a></span>
<br/>.= 
<font color="Maroon" title="c3">d</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>
<br/>.= 
<font color="Maroon" title="c3">d</font>

;<br/><span class="kw">thus </span> <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> = 
 <a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p5">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c2">z</font></span>)</span>,<span class="p5">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T14" target="_self" onmouseover="rs('binari_2/T14')" onmouseout="rh()">Th14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p5">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p0">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c2">z</font></span>)</span>,<span class="p0">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<span class="p4">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <span class="p5">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T14" target="_self" onmouseover="rs('binari_2/T14')" onmouseout="rh()">Th14</a></span>
<br/>.= 
<font color="Maroon" title="c2">z</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_2"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E2:22_2_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E13:22_2_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E14:22_2_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E16:22_2_1"><span class="lab"><font color="Green" title="E29">A23</font></span></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/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:22_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 ; <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/></div><span class="kw">end;</span></div>
<span class="kw">thus </span><a NAME="E3:22"/>
 for <font color="Olive" title="b1">m</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S10" onmouseover="rs('nat_1/S10')" onmouseout="rh()">NAT_1:sch 10</a>(<a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E17">A11</font></span></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/>


</div>
