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

<span class="kw">thus </span><a NAME="E1:70_1_1"/>
 <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  is  <a href="compos_1.html#V7" title="COMPOS_1:attr.7">regular</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  is  <a href="compos_1.html#V8" title="COMPOS_1:attr.8">J/A-independent</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_1.html#D14" title="COMPOS_1:def.14">COMPOS_1:def 14</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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">T</font> =  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font>;<br/>
<a NAME="E1:70_1_1_1"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span>
 
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_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="E1:70_1_1_1_1"/>
(  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="scmfsa10.html#E9"><span class="lab"><font color="Green" title="E9">Lm1</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_1"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</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">  for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><a NAME="E2:70_1_1_1_1_1"/><span class="kw">then </span>
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T17" target="_self" title="SCMFSA10:th.17">Th30</a></span>;<br/><a NAME="E3:70_1_1_1_1_1"/><span class="kw">then </span>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">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="#E1:70_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_1_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ; <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="70_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_2"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><a NAME="E2:70_1_1_1_1_2"/><span class="kw">then </span>
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T18" target="_self" title="SCMFSA10:th.18">Th31</a></span>;<br/><a NAME="E3:70_1_1_1_1_2"/><span class="kw">then </span>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">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="#E1:70_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_1_1_2"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ; <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="70_1_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_3"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><a NAME="E2:70_1_1_1_1_3"/><span class="kw">then </span>
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T19" target="_self" title="SCMFSA10:th.19">Th32</a></span>;<br/><a NAME="E3:70_1_1_1_1_3"/><span class="kw">then </span>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">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="#E1:70_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_1_1_3"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ; <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="70_1_1_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_4"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><a NAME="E2:70_1_1_1_1_4"/><span class="kw">then </span>
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T20" target="_self" title="SCMFSA10:th.20">Th33</a></span>;<br/><a NAME="E3:70_1_1_1_1_4"/><span class="kw">then </span>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">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="#E1:70_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_1_1_4"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ; <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="70_1_1_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_5"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><a NAME="E2:70_1_1_1_1_5"/><span class="kw">then </span>
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T21" target="_self" title="SCMFSA10:th.21">Th34</a></span>;<br/><a NAME="E3:70_1_1_1_1_5"/><span class="kw">then </span>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">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="#E1:70_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_1_1_5"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ; <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="70_1_1_1_1_6"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_6"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><a NAME="E2:70_1_1_1_1_6"/><span class="kw">then </span>
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T22" target="_self" title="SCMFSA10:th.22">Th35</a></span>;<br/><a NAME="E3:70_1_1_1_1_6"/><span class="kw">then </span>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">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="#E1:70_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_1_1_6"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ; <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="70_1_1_1_1_7"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_7"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:70_1_1_1_1_7"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c3">i2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T35" title="SCMFSA_2:th.35">SCMFSA_2:35</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c4">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">k</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><span class="kw">assume </span><a NAME="E4:70_1_1_1_1_7"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
<font color="Maroon" title="c4">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 ; <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="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><br/><a NAME="E5:70_1_1_1_1_7"/>
 for <font color="Olive" title="b1">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> holds <br/><font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">f</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_1_1_7_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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="c5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> implies <font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:70_1_1_1_1_7_1"/>
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span>
 ; <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="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">J</font> being   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><span class="kw"> such that </span><br/><a NAME="E3:70_1_1_1_1_7_1"/><span class="lab"><font color="Green" title="E50">A5</font></span>: 
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c6">J</font>
 <span class="kw">and </span><br/><a NAME="E4:70_1_1_1_1_7_1"/><span class="lab"><font color="Green" title="E51">A6</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c6">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font>
 ;<br/>
<span class="kw">thus </span><a NAME="E5:70_1_1_1_1_7_1"/>
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:70_1_1_1_1_7"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="txt" href="#E3:70_1_1_1_1_7_1"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="txt" href="#E4:70_1_1_1_1_7_1"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="compos_1.html#D12" title="COMPOS_1:def.12">COMPOS_1:def 12</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="E6:70_1_1_1_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#D12" title="CARD_3:def.12">CARD_3:def 12</a></span>;<br/><a NAME="E7:70_1_1_1_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_1_1_7"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="scmfsa10.html#T23" target="_self" title="SCMFSA10:th.23">Th36</a></span>;<br/><a NAME="E8:70_1_1_1_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E9:70_1_1_1_1_7"/>
<span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:70_1_1_1_1_7"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="scmfsa10.html#T30" target="_self" title="SCMFSA10:th.30">Th53</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="70_1_1_1_1_8"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_8"/><span class="lab"><font color="Green" title="E47">A7</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c4">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:70_1_1_1_1_8"/><span class="lab"><font color="Green" title="E48">A8</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c3">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T36" title="SCMFSA_2:th.36">SCMFSA_2:36</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c5">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">k</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><span class="kw">assume </span><a NAME="E4:70_1_1_1_1_8"/><span class="lab"><font color="Green" title="E49">A9</font></span>: 
<font color="Maroon" title="c5">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 ; <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="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><br/><a NAME="E5:70_1_1_1_1_8"/>
 for <font color="Olive" title="b1">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> holds <br/><font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">f</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_1_1_8_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> implies <font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:70_1_1_1_1_8_1"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span>
 ; <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="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">J</font> being   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><span class="kw"> such that </span><br/><a NAME="E3:70_1_1_1_1_8_1"/><span class="lab"><font color="Green" title="E50">A10</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c7">J</font>
 <span class="kw">and </span><br/><a NAME="E4:70_1_1_1_1_8_1"/><span class="lab"><font color="Green" title="E51">A11</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font>
 ;<br/>
<span class="kw">thus </span><a NAME="E5:70_1_1_1_1_8_1"/>
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:70_1_1_1_1_8"><span class="lab"><font color="Green" title="E49">A9</font></span></a>, <a class="txt" href="#E3:70_1_1_1_1_8_1"><span class="lab"><font color="Green" title="E50">A10</font></span></a>, <a class="txt" href="#E4:70_1_1_1_1_8_1"><span class="lab"><font color="Green" title="E51">A11</font></span></a>, <a class="ref" href="compos_1.html#D12" title="COMPOS_1:def.12">COMPOS_1:def 12</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="E6:70_1_1_1_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#D12" title="CARD_3:def.12">CARD_3:def 12</a></span>;<br/><a NAME="E7:70_1_1_1_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_1_1_8"><span class="lab"><font color="Green" title="E47">A7</font></span></a>, <a class="ref" href="scmfsa10.html#T24" target="_self" title="SCMFSA10:th.24">Th37</a></span>;<br/><a NAME="E8:70_1_1_1_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E9:70_1_1_1_1_8"/>
<span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:70_1_1_1_1_8"><span class="lab"><font color="Green" title="E48">A8</font></span></a>, <a class="ref" href="scmfsa10.html#T31" target="_self" title="SCMFSA10:th.31">Th54</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="70_1_1_1_1_9"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_9"/><span class="lab"><font color="Green" title="E47">A12</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c4">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:70_1_1_1_1_9"/><span class="lab"><font color="Green" title="E48">A13</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c3">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T37" title="SCMFSA_2:th.37">SCMFSA_2:37</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c5">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">k</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><span class="kw">assume </span><a NAME="E4:70_1_1_1_1_9"/><span class="lab"><font color="Green" title="E49">A14</font></span>: 
<font color="Maroon" title="c5">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 ; <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="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><br/><a NAME="E5:70_1_1_1_1_9"/>
 for <font color="Olive" title="b1">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> holds <br/><font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">f</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_1_1_9_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> implies <font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:70_1_1_1_1_9_1"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span>
 ; <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="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">J</font> being   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><span class="kw"> such that </span><br/><a NAME="E3:70_1_1_1_1_9_1"/><span class="lab"><font color="Green" title="E50">A15</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c7">J</font>
 <span class="kw">and </span><br/><a NAME="E4:70_1_1_1_1_9_1"/><span class="lab"><font color="Green" title="E51">A16</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font>
 ;<br/>
<span class="kw">thus </span><a NAME="E5:70_1_1_1_1_9_1"/>
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:70_1_1_1_1_9"><span class="lab"><font color="Green" title="E49">A14</font></span></a>, <a class="txt" href="#E3:70_1_1_1_1_9_1"><span class="lab"><font color="Green" title="E50">A15</font></span></a>, <a class="txt" href="#E4:70_1_1_1_1_9_1"><span class="lab"><font color="Green" title="E51">A16</font></span></a>, <a class="ref" href="compos_1.html#D12" title="COMPOS_1:def.12">COMPOS_1:def 12</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="E6:70_1_1_1_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#D12" title="CARD_3:def.12">CARD_3:def 12</a></span>;<br/><a NAME="E7:70_1_1_1_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_1_1_9"><span class="lab"><font color="Green" title="E47">A12</font></span></a>, <a class="ref" href="scmfsa10.html#T25" target="_self" title="SCMFSA10:th.25">Th38</a></span>;<br/><a NAME="E8:70_1_1_1_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E9:70_1_1_1_1_9"/>
<span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:70_1_1_1_1_9"><span class="lab"><font color="Green" title="E48">A13</font></span></a>, <a class="ref" href="scmfsa10.html#T32" target="_self" title="SCMFSA10:th.32">Th56</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="70_1_1_1_1_10"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_10"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><a NAME="E2:70_1_1_1_1_10"/><span class="kw">then </span>
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T26" target="_self" title="SCMFSA10:th.26">Th39</a></span>;<br/><a NAME="E3:70_1_1_1_1_10"/><span class="kw">then </span>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">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="#E1:70_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_1_1_10"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ; <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="70_1_1_1_1_11"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_11"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><a NAME="E2:70_1_1_1_1_11"/><span class="kw">then </span>
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T27" target="_self" title="SCMFSA10:th.27">Th40</a></span>;<br/><a NAME="E3:70_1_1_1_1_11"/><span class="kw">then </span>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">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="#E1:70_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_1_1_11"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ; <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="70_1_1_1_1_12"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_12"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><a NAME="E2:70_1_1_1_1_12"/><span class="kw">then </span>
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T28" target="_self" title="SCMFSA10:th.28">Th41</a></span>;<br/><a NAME="E3:70_1_1_1_1_12"/><span class="kw">then </span>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">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="#E1:70_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_1_1_12"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ; <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="70_1_1_1_1_13"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_1_1_13"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 ; <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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/><div class="add"><a NAME="E2:70_1_1_1_1_13"/><span class="kw">then </span>
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T29" target="_self" title="SCMFSA10:th.29">Th42</a></span>;<br/><a NAME="E3:70_1_1_1_1_13"/><span class="kw">then </span>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">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="#E1:70_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_1_1_13"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 ; <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">let </span><font color="Maroon" title="c1">T</font> be   <a href="compos_1.html#NM3" title="COMPOS_1:NM.3">InsType</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_1.html#D15" title="COMPOS_1:def.15">COMPOS_1:def 15</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">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive">b<sub>3</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font> or  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span> or  not <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> or <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">f1</font>, <font color="Maroon" title="c3">f2</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Maroon" title="c2">f1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font> or  not <font color="Maroon" title="c3">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span> or  not <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">f1</font>,<font color="Olive">b<sub>1</sub></font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> or <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Olive">b<sub>1</sub></font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">f1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font> or  not <font color="Maroon" title="c3">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span> or  not <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> or <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:70_1_1"/><span class="lab"><font color="Green" title="E46">A17</font></span>: 
<font color="Maroon" title="c2">f1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font>
 <span class="kw">and </span><br/><a NAME="E3:70_1_1"/><span class="lab"><font color="Green" title="E47">A18</font></span>: 
<font color="Maroon" title="c3">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:70_1_1"/><span class="lab"><font color="Green" title="E48">A19</font></span>: 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_2"><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="E1:70_1_1_2"/>
( <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="scmfsa10.html#E9"><span class="lab"><font color="Green" title="E9">Lm1</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_2_1"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_2_1"/>
( <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span><br/><div class="add"><a NAME="E2:70_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A20</font></span>: 
 <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T17" target="_self" title="SCMFSA10:th.17">Th30</a>, <a class="ref" href="scmfsa10.html#T18" target="_self" title="SCMFSA10:th.18">Th31</a>, <a class="ref" href="scmfsa10.html#T19" target="_self" title="SCMFSA10:th.19">Th32</a>, <a class="ref" href="scmfsa10.html#T20" target="_self" title="SCMFSA10:th.20">Th33</a>, <a class="ref" href="scmfsa10.html#T21" target="_self" title="SCMFSA10:th.21">Th34</a>, <a class="ref" href="scmfsa10.html#T22" target="_self" title="SCMFSA10:th.22">Th35</a>, <a class="ref" href="scmfsa10.html#T26" target="_self" title="SCMFSA10:th.26">Th39</a>, <a class="ref" href="scmfsa10.html#T27" target="_self" title="SCMFSA10:th.27">Th40</a>, <a class="ref" href="scmfsa10.html#T28" target="_self" title="SCMFSA10:th.28">Th41</a>, <a class="ref" href="scmfsa10.html#T29" target="_self" title="SCMFSA10:th.29">Th42</a></span>;<br/><span class="kw">then </span><font color="Maroon" title="c2">f1</font> = 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:70_1_1"><span class="lab"><font color="Green" title="E46">A17</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c3">f2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:70_1_1"><span class="lab"><font color="Green" title="E47">A18</font></span></a>, <a class="txt" href="#E2:70_1_1_2_1"><span class="lab"><font color="Green" title="E49">A20</font></span></a>, <a class="ref" href="card_3.html#T10" title="CARD_3:th.10">CARD_3:10</a>, <a class="ref" href="card_3.html#T106" title="CARD_3:th.106">CARD_3:106</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>
;<br/><span class="kw">hence </span><a NAME="E4:70_1_1_2_1"/>
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:70_1_1"><span class="lab"><font color="Green" title="E48">A19</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="70_1_1_2_2"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_2_2"/><span class="lab"><font color="Green" title="E49">A21</font></span>: 
<font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c5">J</font> = <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> as   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:70_1_1"><span class="lab"><font color="Green" title="E48">A19</font></span></a></span>;<br/><a NAME="E3:70_1_1_2_2"/><span class="lab"><font color="Green" title="E50">A22</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c5">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_2"><span class="lab"><font color="Green" title="E49">A21</font></span></a>, <a class="ref" href="recdef_2.html#D1" title="RECDEF_2:def.1">RECDEF_2:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E5:70_1_1_2_2"/><span class="lab"><font color="Green" title="E51">A23</font></span>: 
<font color="Maroon" title="c5">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c6">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T35" title="SCMFSA_2:th.35">SCMFSA_2:35</a></span>;<br/><a NAME="E6:70_1_1_2_2"/><span class="lab"><font color="Green" title="E52">A24</font></span>: 
<font color="Maroon" title="c4">p</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="#E5:70_1_1_2_2"><span class="lab"><font color="Green" title="E51">A23</font></span></a>, <a class="ref" href="mcart_1.html#T25" title="MCART_1:th.25">MCART_1:25</a></span>;<br/><a NAME="E7:70_1_1_2_2"/><span class="lab"><font color="Green" title="E53">A25</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:70_1_1"><span class="lab"><font color="Green" title="E47">A18</font></span></a>, <a class="ref" href="card_3.html#T9" title="CARD_3:th.9">CARD_3:9</a></span>;<br/><a NAME="E8:70_1_1_2_2"/><span class="lab"><font color="Green" title="E54">A26</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_2"><span class="lab"><font color="Green" title="E49">A21</font></span></a>, <a class="txt" href="#E7:70_1_1_2_2"><span class="lab"><font color="Green" title="E53">A25</font></span></a>, <a class="ref" href="scmfsa10.html#T23" target="_self" title="SCMFSA10:th.23">Th36</a></span>;<br/><a NAME="E9:70_1_1_2_2"/><span class="kw">then </span>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E10:70_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:70_1_1_2_2"><span class="lab"><font color="Green" title="E53">A25</font></span></a>, <a class="txt" href="#E3:70_1_1"><span class="lab"><font color="Green" title="E47">A18</font></span></a>, <a class="ref" href="card_3.html#T9" title="CARD_3:th.9">CARD_3:9</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">l</font> = <font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:70_1_1_2_2"><span class="lab"><font color="Green" title="E51">A23</font></span></a>, <a class="txt" href="#E1:70_1_1_2_2"><span class="lab"><font color="Green" title="E49">A21</font></span></a>, <a class="txt" href="#E3:70_1_1_2_2"><span class="lab"><font color="Green" title="E50">A22</font></span></a>, <a class="ref" href="scmfsa10.html#T30" target="_self" title="SCMFSA10:th.30">Th53</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c8">I</font> = <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>;<br/><a NAME="E12:70_1_1_2_2"/>
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c7">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_2"><span class="lab"><font color="Green" title="E49">A21</font></span></a>, <a class="txt" href="#E8:70_1_1_2_2"><span class="lab"><font color="Green" title="E54">A26</font></span></a>, <a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">I</font> = <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> as   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><a NAME="E14:70_1_1_2_2"/>
<font color="Maroon" title="c3">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c9">I</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E15:70_1_1_2_2"/>
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:70_1_1_2_2"><span class="lab"><font color="Green" title="E52">A24</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="70_1_1_2_3"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_2_3"/><span class="lab"><font color="Green" title="E49">A27</font></span>: 
<font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c5">J</font> = <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> as   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:70_1_1"><span class="lab"><font color="Green" title="E48">A19</font></span></a></span>;<br/><a NAME="E3:70_1_1_2_3"/><span class="lab"><font color="Green" title="E50">A28</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c5">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="recdef_2.html#D1" title="RECDEF_2:def.1">RECDEF_2:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c7">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E5:70_1_1_2_3"/><span class="lab"><font color="Green" title="E51">A29</font></span>: 
<font color="Maroon" title="c5">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c6">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_3"><span class="lab"><font color="Green" title="E49">A27</font></span></a>, <a class="ref" href="scmfsa_2.html#T36" title="SCMFSA_2:th.36">SCMFSA_2:36</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c8">A</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <span class="kw"> such that </span><br/><a NAME="E7:70_1_1_2_3"/><span class="lab"><font color="Green" title="E52">A30</font></span>: 
( <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c6">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">A</font> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <font color="Maroon" title="c6">i1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#D14" title="SCMFSA_2:def.14">SCMFSA_2:def 14</a></span>;<br/><a NAME="E8:70_1_1_2_3"/><span class="lab"><font color="Green" title="E53">A31</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c7">a</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:70_1_1_2_3"><span class="lab"><font color="Green" title="E51">A29</font></span></a>, <a class="txt" href="#E7:70_1_1_2_3"><span class="lab"><font color="Green" title="E52">A30</font></span></a>, <a class="ref" href="mcart_1.html#T25" title="MCART_1:th.25">MCART_1:25</a></span>;<br/><a NAME="E9:70_1_1_2_3"/><span class="lab"><font color="Green" title="E54">A32</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:70_1_1"><span class="lab"><font color="Green" title="E47">A18</font></span></a>, <a class="ref" href="card_3.html#T9" title="CARD_3:th.9">CARD_3:9</a></span>;<br/><a NAME="E10:70_1_1_2_3"/><span class="lab"><font color="Green" title="E55">A33</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_3"><span class="lab"><font color="Green" title="E49">A27</font></span></a>, <a class="txt" href="#E9:70_1_1_2_3"><span class="lab"><font color="Green" title="E54">A32</font></span></a>, <a class="ref" href="scmfsa10.html#T24" target="_self" title="SCMFSA10:th.24">Th37</a></span>;<br/><a NAME="E11:70_1_1_2_3"/><span class="kw">then </span>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E12:70_1_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:70_1_1_2_3"><span class="lab"><font color="Green" title="E54">A32</font></span></a>, <a class="txt" href="#E3:70_1_1"><span class="lab"><font color="Green" title="E47">A18</font></span></a>, <a class="ref" href="card_3.html#T9" title="CARD_3:th.9">CARD_3:9</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">l</font> = <font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:70_1_1_2_3"><span class="lab"><font color="Green" title="E51">A29</font></span></a>, <a class="txt" href="#E3:70_1_1_2_3"><span class="lab"><font color="Green" title="E50">A28</font></span></a>, <a class="ref" href="scmfsa10.html#T31" target="_self" title="SCMFSA10:th.31">Th54</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c10">I</font> = <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>;<br/><a NAME="E14:70_1_1_2_3"/>
<font color="Maroon" title="c3">f2</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="c9">l</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="#E10:70_1_1_2_3"><span class="lab"><font color="Green" title="E55">A33</font></span></a>, <a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><a NAME="E15:70_1_1_2_3"/><span class="kw">then </span>
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c9">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_3"><span class="lab"><font color="Green" title="E49">A27</font></span></a>, <a class="txt" href="#E8:70_1_1_2_3"><span class="lab"><font color="Green" title="E53">A31</font></span></a>, <a class="ref" href="scmfsa10.html#T7" target="_self" title="SCMFSA10:th.7">Th15</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">I</font> = <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> as   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><a NAME="E17:70_1_1_2_3"/><span class="lab"><font color="Green" title="E56">A34</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c11">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="recdef_2.html#D1" title="RECDEF_2:def.1">RECDEF_2:def 1</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c12">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c13">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E19:70_1_1_2_3"/><span class="lab"><font color="Green" title="E57">A35</font></span>: 
<font color="Maroon" title="c11">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c12">i2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_3"><span class="lab"><font color="Green" title="E49">A27</font></span></a>, <a class="txt" href="#E17:70_1_1_2_3"><span class="lab"><font color="Green" title="E56">A34</font></span></a>, <a class="ref" href="scmfsa_2.html#T36" title="SCMFSA_2:th.36">SCMFSA_2:36</a></span>;<br/><span class="kw">thus </span><a NAME="E20:70_1_1_2_3"/>
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:70_1_1_2_3"><span class="lab"><font color="Green" title="E57">A35</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="70_1_1_2_4"><span class="kw">suppose </span></a><a NAME="E1:70_1_1_2_4"/><span class="lab"><font color="Green" title="E49">A36</font></span>: 
<font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c5">J</font> = <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> as   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:70_1_1"><span class="lab"><font color="Green" title="E48">A19</font></span></a></span>;<br/><a NAME="E3:70_1_1_2_4"/><span class="lab"><font color="Green" title="E50">A37</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c5">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="recdef_2.html#D1" title="RECDEF_2:def.1">RECDEF_2:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c7">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E5:70_1_1_2_4"/><span class="lab"><font color="Green" title="E51">A38</font></span>: 
<font color="Maroon" title="c5">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c6">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_4"><span class="lab"><font color="Green" title="E49">A36</font></span></a>, <a class="ref" href="scmfsa_2.html#T37" title="SCMFSA_2:th.37">SCMFSA_2:37</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c8">A</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <span class="kw"> such that </span><br/><a NAME="E7:70_1_1_2_4"/><span class="lab"><font color="Green" title="E52">A39</font></span>: 
( <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c6">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">A</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c6">i1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#D15" title="SCMFSA_2:def.15">SCMFSA_2:def 15</a></span>;<br/><a NAME="E8:70_1_1_2_4"/><span class="lab"><font color="Green" title="E53">A40</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c7">a</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:70_1_1_2_4"><span class="lab"><font color="Green" title="E51">A38</font></span></a>, <a class="txt" href="#E7:70_1_1_2_4"><span class="lab"><font color="Green" title="E52">A39</font></span></a>, <a class="ref" href="mcart_1.html#T25" title="MCART_1:th.25">MCART_1:25</a></span>;<br/><a NAME="E9:70_1_1_2_4"/><span class="lab"><font color="Green" title="E54">A41</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:70_1_1"><span class="lab"><font color="Green" title="E47">A18</font></span></a>, <a class="ref" href="card_3.html#T9" title="CARD_3:th.9">CARD_3:9</a></span>;<br/><a NAME="E10:70_1_1_2_4"/><span class="lab"><font color="Green" title="E55">A42</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_4"><span class="lab"><font color="Green" title="E49">A36</font></span></a>, <a class="txt" href="#E9:70_1_1_2_4"><span class="lab"><font color="Green" title="E54">A41</font></span></a>, <a class="ref" href="scmfsa10.html#T25" target="_self" title="SCMFSA10:th.25">Th38</a></span>;<br/><a NAME="E11:70_1_1_2_4"/><span class="kw">then </span>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E12:70_1_1_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:70_1_1_2_4"><span class="lab"><font color="Green" title="E54">A41</font></span></a>, <a class="txt" href="#E3:70_1_1"><span class="lab"><font color="Green" title="E47">A18</font></span></a>, <a class="ref" href="card_3.html#T9" title="CARD_3:th.9">CARD_3:9</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">l</font> = <font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:70_1_1_2_4"><span class="lab"><font color="Green" title="E51">A38</font></span></a>, <a class="txt" href="#E3:70_1_1_2_4"><span class="lab"><font color="Green" title="E50">A37</font></span></a>, <a class="ref" href="scmfsa10.html#T32" target="_self" title="SCMFSA10:th.32">Th56</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c10">I</font> = <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>;<br/><a NAME="E14:70_1_1_2_4"/>
<font color="Maroon" title="c3">f2</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="c9">l</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="#E10:70_1_1_2_4"><span class="lab"><font color="Green" title="E55">A42</font></span></a>, <a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><a NAME="E15:70_1_1_2_4"/><span class="kw">then </span>
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c9">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_4"><span class="lab"><font color="Green" title="E49">A36</font></span></a>, <a class="txt" href="#E8:70_1_1_2_4"><span class="lab"><font color="Green" title="E53">A40</font></span></a>, <a class="ref" href="scmfsa10.html#T8" target="_self" title="SCMFSA10:th.8">Th16</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">I</font> = <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> as   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><a NAME="E17:70_1_1_2_4"/><span class="lab"><font color="Green" title="E56">A43</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c11">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="recdef_2.html#D1" title="RECDEF_2:def.1">RECDEF_2:def 1</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c12">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c13">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E19:70_1_1_2_4"/><span class="lab"><font color="Green" title="E57">A44</font></span>: 
<font color="Maroon" title="c11">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c12">i2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1_2_4"><span class="lab"><font color="Green" title="E49">A36</font></span></a>, <a class="txt" href="#E17:70_1_1_2_4"><span class="lab"><font color="Green" title="E56">A43</font></span></a>, <a class="ref" href="scmfsa_2.html#T37" title="SCMFSA_2:th.37">SCMFSA_2:37</a></span>;<br/><span class="kw">thus </span><a NAME="E20:70_1_1_2_4"/>
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c4">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:70_1_1_2_4"><span class="lab"><font color="Green" title="E57">A44</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>

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