<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" 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="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  ex <font color="Olive" title="b2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st  <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<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="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c1">m</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">i</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st  <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">a</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#K6" title="MARGREL1:func.6">BOOLEAN</a>, <font color="Maroon" title="c4">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> <span class="kw"> such that </span><br/><a NAME="E2:39"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
 <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T117" title="FINSEQ_2:th.117">FINSEQ_2:117</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:39_1_1"/>
( <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:39_1_1_1"/>
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st  <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">m</font> = <font color="Maroon" title="c1">m</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> ;<br/><a NAME="E3:39_1_1_1"/>
 for <font color="Olive" title="b1">j</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">j</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="c5">m</font> holds <br/><span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:39_1_1_1_1"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">j</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="c5">m</font> implies <span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:39_1_1_1_1"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<font color="Maroon" title="c6">j</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="c5">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">j</font> = <font color="Maroon" title="c6">j</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> ;<br/>
<a NAME="E4:39_1_1_1_1"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">j</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39_1_1_1_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E5:39_1_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/>
<a NAME="E6:39_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A5</font></span>: 
<font color="Maroon" title="c7">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39_1_1_1_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E7:39_1_1_1_1"/><span class="lab"><font color="Green" title="E32">A6</font></span>: 
<font color="Maroon" title="c7">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39_1_1_1_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E8:39_1_1_1_1"/>
<font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/>
<a NAME="E9:39_1_1_1_1"/><span class="kw">then </span>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c7">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:39_1_1_1_1"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> = 
<span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39_1_1_1_1"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="finseq_4.html#T15" title="FINSEQ_4:th.15">FINSEQ_4:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39_1_1_1_1"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="txt" href="#E7:39_1_1_1_1"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="ref" href="binari_4.html#T32" target="_self" title="BINARI_4:th.32">Th32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_1_1_1_1"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E4:39_1_1_1_1"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="txt" href="#E7:39_1_1_1_1"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="ref" href="finseq_4.html#T15" title="FINSEQ_4:th.15">FINSEQ_4:15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E11:39_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E6:39_1_1_1_1"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E4:39_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c2">i</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T119" title="FINSEQ_2:th.119">FINSEQ_2:119</a></span>;<br/><span class="kw">hence </span><a NAME="E5:39_1_1_1"/>
 ex <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st  <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E27">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:39_1_1_2"/><span class="lab"><font color="Green" title="E28">A7</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st  <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">c</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> <span class="kw"> such that </span><br/><a NAME="E3:39_1_1_2"/><span class="lab"><font color="Green" title="E29">A8</font></span>: 
 <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">c</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T97" title="FINSEQ_2:th.97">FINSEQ_2:97</a></span>;<br/><a NAME="E4:39_1_1_2"/><span class="lab"><font color="Green" title="E30">A9</font></span>: 
 <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">c</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_1_1_2"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="ref" href="finseq_1.html#T34" title="FINSEQ_1:th.34">FINSEQ_1:34</a></span>;<br/><a NAME="E5:39_1_1_2"/>
 <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_1_1_2"><span class="lab"><font color="Green" title="E28">A7</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:39_1_1_2"/>
 ex <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st  <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39_1_1_2"><span class="lab"><font color="Green" title="E30">A9</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><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="E4:39"/>
 ex <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st  <a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,<font color="Maroon" title="c2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" title="BINARI_4:func.2">2sComplement</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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