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<span class="kw">let </span><font color="Maroon" title="c1">n</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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of <font color="Maroon" title="c1">n</font>, <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>   st <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b1">x</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  &amp; <span class="p1">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<font color="Olive" title="b1">x</font>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Olive" title="b2">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of <font color="Maroon" title="c1">n</font>, <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"> ( <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">x</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  &amp; <span class="p1">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  implies <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:22"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">and </span><br/><a NAME="E2:22"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">and </span><br/><a NAME="E3:22"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<span class="p1">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</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" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span><br/>

<a NAME="E4:22"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</a></span>;<br/>
<a NAME="E5:22"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</a></span>;<br/>
<a NAME="E6:22"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</a></span>;<br/>
<a NAME="E7:22"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_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">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">i</font> be   <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" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> implies <font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c5">z</font> = <font color="Maroon" title="c4">i</font> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ;<br/><span class="kw">assume </span><a NAME="E2:22_1"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</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" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span><br/><a NAME="E3:22_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A9</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T1" onmouseover="rs('finseq_1/T1')" onmouseout="rh()">FINSEQ_1:1</a></span>;<br/><a NAME="E4:22_1"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="finseq_1.html#T1" onmouseover="rs('finseq_1/T1')" onmouseout="rh()">FINSEQ_1:1</a></span>;<br/><a NAME="E5:22_1"/><span class="lab"><font color="Green" title="E25">A11</font></span>: 
<font color="Maroon" title="c3">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <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="txt" href="#E1:22"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_1_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"> <font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:22_1_1_1"/>
( <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c4">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_1_1_1_1"/><span class="lab"><font color="Green" title="E26">A12</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.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"> <font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:22_1_1_1_1"/><span class="lab"><font color="Green" title="E27">A13</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T14" onmouseover="rs('nat_1/T14')" onmouseout="rh()">NAT_1:14</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_1_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"> <font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:22_1_1_1_1_1_1"/>
( <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1_1_1"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.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"> <font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:22_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="binarith.html#D2" onmouseover="rs('binarith/D2')" onmouseout="rh()">BINARITH:def 2</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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E28">A14</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</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"> <font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:22_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E29">A15</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</a></span>;<br/><a NAME="E3:22_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
<span class="p1">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">i</font> <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="txt" href="#E1:22_1_1_1_1"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="binarith.html#D2" onmouseover="rs('binarith/D2')" onmouseout="rh()">BINARITH:def 2</a></span>;<br/><a NAME="E4:22_1_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A17</font></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">n</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">i</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> (<font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 
 ;<br/><a NAME="E5:22_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E32">A18</font></span>: 
1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><a NAME="E6:22_1_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A19</font></span>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T1" onmouseover="rs('finseq_1/T1')" onmouseout="rh()">FINSEQ_1:1</a></span>;<br/><span class="p1">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</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"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E1:22_1_1_1_1"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="binari_3.html#T20" target="_self" onmouseover="rs('binari_3/T20')" onmouseout="rh()">Th20</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"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E2:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</a></span>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</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> <font color="Maroon" title="c1">n</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="binarith.html#D1" onmouseover="rs('binarith/D1')" onmouseout="rh()">BINARITH:def 1</a></span>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="binari_2.html#T6" onmouseover="rs('binari_2/T6')" onmouseout="rh()">BINARI_2:6</a></span>
<br/>.= 
 <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 

;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A20</font></span>:  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  = 
<span class="p1">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:22"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E1:22_1_1_1_1"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E5:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">i</font></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="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">i</font></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"><font color="Maroon" title="c2">x</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">i</font></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> (<font color="Maroon" title="c2">x</font>,<span class="p4">(<span class="default"><a href="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1_1_1"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E1:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E3:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E4:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <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"><font color="Maroon" title="c2">x</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">i</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="binari_2.html#K1" title="BINARI_2:func.1">Bin1</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A16</font></span></a></span>
;<br/><span class="kw">thus </span><font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> = 
<font color="Maroon" title="c2">x</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">z</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</a></span>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:22_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="margrel1.html#T12" onmouseover="rs('margrel1/T12')" onmouseout="rh()">MARGREL1:12</a></span>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E5:22_1"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">z</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E22">A8</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="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</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="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:22_1_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_1_1_1_2"/><span class="lab"><font color="Green" title="E26">A21</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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"> <font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:22_1_1_1_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="finseq_1.html#T1" onmouseover="rs('finseq_1/T1')" onmouseout="rh()">FINSEQ_1:1</a></span>;<br/><a NAME="E3:22_1_1_1_2"/><span class="kw">then </span>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">i</font>
 ;<br/><a NAME="E4:22_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A22</font></span>: 
 not <font color="Maroon" title="c4">i</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ;<br/><span class="kw">thus </span><font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> = 
<font color="Maroon" title="c2">x</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">z</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</a></span>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E1:22_1_1_1_2"><span class="lab"><font color="Green" title="E26">A21</font></span></a>, <a class="txt" href="#E4:22_1_1_1_2"><span class="lab"><font color="Green" title="E27">A22</font></span></a>, <a class="ref" href="binari_3.html#T19" target="_self" onmouseover="rs('binari_3/T19')" onmouseout="rh()">Th19</a></span>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E5:22_1"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">z</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E22">A8</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="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</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="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E7:22_1"/>
<font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</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"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E9:22"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binarith.html#K3" title="BINARITH:func.3">'not'</a> <font color="Maroon" title="c3">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T119" onmouseover="rs('finseq_2/T119')" onmouseout="rh()">FINSEQ_2:119</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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