<?xml version="1.0"?>
<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="ami_3.html#K1" title="AMI_3:func.1">SCM</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="amistd_2.html#D2" onmouseover="rs('amistd_2/D2')" onmouseout="rh()">AMISTD_2:def 2</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">I</font> is  <a href="amistd_2.html#V1" title="AMISTD_2:attr.1">with_explicit_jumps</a> </span><br/>

<span class="kw">thus </span><a NAME="E1:42_1_1"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="amistd_2.html#D1" onmouseover="rs('amistd_2/D1')" onmouseout="rh()">AMISTD_2:def 1</a>,<a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">proj2</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="42_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font> or <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:42_1_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:42_1_1_1_1"/>
( <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K2" title="AMI_3:func.2">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K3" title="AMI_3:func.3">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K6" title="AMI_3:func.6">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">SCM-goto</a> <font color="Olive" title="b1">k</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> ex <font color="Olive" title="b2">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K8" title="AMI_3:func.8">=0_goto</a> <font color="Olive" title="b2">k1</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> ex <font color="Olive" title="b2">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Olive" title="b2">k1</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="ami_3.html#T24" onmouseover="rs('ami_3/T24')" onmouseout="rh()">AMI_3:24</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_1_1_1"/>
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:42_1_1_1_1_1"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="ami_3.html#T26" onmouseover="rs('ami_3/T26')" onmouseout="rh()">AMI_3:26</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_1_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K2" title="AMI_3:func.2">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:42_1_1_1_1_2"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_1_1_3"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K3" title="AMI_3:func.3">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:42_1_1_1_1_3"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_1_1_4"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:42_1_1_1_1_4"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_1_1_5"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:42_1_1_1_1_5"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1_6"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_1_1_6"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K6" title="AMI_3:func.6">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:42_1_1_1_1_6"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1_7"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_1_1_7"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
 ex <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">SCM-goto</a> <font color="Olive" title="b1">k</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c3">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_1_1_7"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">SCM-goto</a> <font color="Maroon" title="c3">k1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1_1_7"><span class="lab"><font color="Green" title="E16">A2</font></span></a></span>;<br/><a NAME="E4:42_1_1_1_1_7"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c3">k1</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></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"><font color="Maroon" title="c3">k1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T39" onmouseover="rs('finseq_1/T39')" onmouseout="rh()">FINSEQ_1:39</a></span>;<br/><a NAME="E5:42_1_1_1_1_7"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">SCM-goto</a> <font color="Maroon" title="c3">k1</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"><font color="Maroon" title="c3">k1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_6.html#T16" target="_self" onmouseover="rs('ami_6/T16')" onmouseout="rh()">Th16</a></span>;<br/><span class="kw">hence </span><a NAME="E6:42_1_1_1_1_7"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E3:42_1_1_1_1_7"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:42_1_1_1_1_7"><span class="lab"><font color="Green" title="E18">A4</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1_8"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_1_1_8"/><span class="lab"><font color="Green" title="E16">A5</font></span>: 
 ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> ex <font color="Olive" title="b2">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K8" title="AMI_3:func.8">=0_goto</a> <font color="Olive" title="b2">k1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a>, <font color="Maroon" title="c4">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_1_1_8"/><span class="lab"><font color="Green" title="E17">A6</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="ami_3.html#K8" title="AMI_3:func.8">=0_goto</a> <font color="Maroon" title="c4">k1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1_1_8"><span class="lab"><font color="Green" title="E16">A5</font></span></a></span>;<br/><a NAME="E4:42_1_1_1_1_8"/><span class="lab"><font color="Green" title="E18">A7</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c4">k1</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></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"><font color="Maroon" title="c4">k1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T39" onmouseover="rs('finseq_1/T39')" onmouseout="rh()">FINSEQ_1:39</a></span>;<br/><a NAME="E5:42_1_1_1_1_8"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="ami_3.html#K8" title="AMI_3:func.8">=0_goto</a> <font color="Maroon" title="c4">k1</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"><font color="Maroon" title="c4">k1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_6.html#T18" target="_self" onmouseover="rs('ami_6/T18')" onmouseout="rh()">Th18</a></span>;<br/><span class="kw">hence </span><a NAME="E6:42_1_1_1_1_8"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E3:42_1_1_1_1_8"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E4:42_1_1_1_1_8"><span class="lab"><font color="Green" title="E18">A7</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1_9"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_1_1_9"/><span class="lab"><font color="Green" title="E16">A8</font></span>: 
 ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> ex <font color="Olive" title="b2">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Olive" title="b2">k1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a>, <font color="Maroon" title="c4">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_1_1_9"/><span class="lab"><font color="Green" title="E17">A9</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="ami_3.html#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Maroon" title="c4">k1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1_1_9"><span class="lab"><font color="Green" title="E16">A8</font></span></a></span>;<br/><a NAME="E4:42_1_1_1_1_9"/><span class="lab"><font color="Green" title="E18">A10</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c4">k1</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></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"><font color="Maroon" title="c4">k1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T39" onmouseover="rs('finseq_1/T39')" onmouseout="rh()">FINSEQ_1:39</a></span>;<br/><a NAME="E5:42_1_1_1_1_9"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="ami_3.html#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Maroon" title="c4">k1</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"><font color="Maroon" title="c4">k1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_6.html#T20" target="_self" onmouseover="rs('ami_6/T20')" onmouseout="rh()">Th20</a></span>;<br/><span class="kw">hence </span><a NAME="E6:42_1_1_1_1_9"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E3:42_1_1_1_1_9"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="txt" href="#E4:42_1_1_1_1_9"><span class="lab"><font color="Green" title="E18">A10</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">proj2</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> or <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:42_1_1"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">k</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E4:42_1_1"/><span class="lab"><font color="Green" title="E15">A11</font></span>: 
<font color="Maroon" title="c3">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_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:42_1_1"/><span class="lab"><font color="Green" title="E16">A12</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:42_1_1_2"/>
( <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K2" title="AMI_3:func.2">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K3" title="AMI_3:func.3">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K6" title="AMI_3:func.6">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">SCM-goto</a> <font color="Olive" title="b1">k</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> ex <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K8" title="AMI_3:func.8">=0_goto</a> <font color="Olive" title="b2">k</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> ex <font color="Olive" title="b2">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Olive" title="b2">k1</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="ami_3.html#T24" onmouseover="rs('ami_3/T24')" onmouseout="rh()">AMI_3:24</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2_1"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_1"/>
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><a NAME="E2:42_1_1_2_1"/><span class="kw">then </span>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 ;<br/><span class="kw">hence </span><a NAME="E3:42_1_1_2_1"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2_2"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K2" title="AMI_3:func.2">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_2_2"/><span class="lab"><font color="Green" title="E17">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="ami_3.html#K2" title="AMI_3:func.2">:=</a> <font color="Maroon" title="c5">b</font>
 ;<br/><a NAME="E4:42_1_1_2_2"/>
<font color="Maroon" title="c3">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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E3:42_1_1_2_2"><span class="lab"><font color="Green" title="E17">A13</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:42_1_1_2_2"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2_3"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_3"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K3" title="AMI_3:func.3">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_2_3"/><span class="lab"><font color="Green" title="E17">A14</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K3" title="AMI_3:func.3">AddTo</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)
 ;<br/><a NAME="E4:42_1_1_2_3"/>
<font color="Maroon" title="c3">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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E3:42_1_1_2_3"><span class="lab"><font color="Green" title="E17">A14</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:42_1_1_2_3"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2_4"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_4"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_2_4"/><span class="lab"><font color="Green" title="E17">A15</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">SubFrom</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)
 ;<br/><a NAME="E4:42_1_1_2_4"/>
<font color="Maroon" title="c3">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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E3:42_1_1_2_4"><span class="lab"><font color="Green" title="E17">A15</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:42_1_1_2_4"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2_5"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_5"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_2_5"/><span class="lab"><font color="Green" title="E17">A16</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">MultBy</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)
 ;<br/><a NAME="E4:42_1_1_2_5"/>
<font color="Maroon" title="c3">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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E3:42_1_1_2_5"><span class="lab"><font color="Green" title="E17">A16</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:42_1_1_2_5"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2_6"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_6"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K6" title="AMI_3:func.6">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_2_6"/><span class="lab"><font color="Green" title="E17">A17</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K6" title="AMI_3:func.6">Divide</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)
 ;<br/><a NAME="E4:42_1_1_2_6"/>
<font color="Maroon" title="c3">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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E3:42_1_1_2_6"><span class="lab"><font color="Green" title="E17">A17</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:42_1_1_2_6"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2_7"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_7"/>
 ex <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">SCM-goto</a> <font color="Olive" title="b1">k</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_2_7"/><span class="lab"><font color="Green" title="E17">A18</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">SCM-goto</a> <font color="Maroon" title="c4">k1</font>
 ;<br/><a NAME="E4:42_1_1_2_7"/><span class="lab"><font color="Green" title="E18">A19</font></span>: 
 <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</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="c4">k1</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="#E3:42_1_1_2_7"><span class="lab"><font color="Green" title="E17">A18</font></span></a></span>;<br/><a NAME="E5:42_1_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="finseq_1.html#T90" onmouseover="rs('finseq_1/T90')" onmouseout="rh()">FINSEQ_1:90</a></span>;<br/><a NAME="E6:42_1_1_2_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A20</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1_2_7"><span class="lab"><font color="Green" title="E18">A19</font></span></a>, <a class="txt" href="#E5:42_1_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a></span>;<br/><a NAME="E7:42_1_1_2_7"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</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"><font color="Maroon" title="c4">k1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42_1_1_2_7"><span class="lab"><font color="Green" title="E17">A18</font></span></a>, <a class="ref" href="ami_6.html#T16" target="_self" onmouseover="rs('ami_6/T16')" onmouseout="rh()">Th16</a></span>;<br/><span class="kw">hence </span><a NAME="E8:42_1_1_2_7"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:42_1_1_2_7"><span class="lab"><font color="Green" title="E19">A20</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2_8"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_8"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> ex <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K8" title="AMI_3:func.8">=0_goto</a> <font color="Olive" title="b2">k</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a>, <font color="Maroon" title="c5">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_2_8"/><span class="lab"><font color="Green" title="E17">A21</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="ami_3.html#K8" title="AMI_3:func.8">=0_goto</a> <font color="Maroon" title="c5">k1</font>
 ;<br/><a NAME="E4:42_1_1_2_8"/><span class="lab"><font color="Green" title="E18">A22</font></span>: 
 <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</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="c5">k1</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="#E3:42_1_1_2_8"><span class="lab"><font color="Green" title="E17">A21</font></span></a></span>;<br/><a NAME="E5:42_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="finseq_1.html#T90" onmouseover="rs('finseq_1/T90')" onmouseout="rh()">FINSEQ_1:90</a></span>;<br/><a NAME="E6:42_1_1_2_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A23</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1_2_8"><span class="lab"><font color="Green" title="E18">A22</font></span></a>, <a class="txt" href="#E5:42_1_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a></span>;<br/><a NAME="E7:42_1_1_2_8"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</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"><font color="Maroon" title="c5">k1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42_1_1_2_8"><span class="lab"><font color="Green" title="E17">A21</font></span></a>, <a class="ref" href="ami_6.html#T18" target="_self" onmouseover="rs('ami_6/T18')" onmouseout="rh()">Th18</a></span>;<br/><span class="kw">hence </span><a NAME="E8:42_1_1_2_8"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:42_1_1_2_8"><span class="lab"><font color="Green" title="E19">A23</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2_9"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_9"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a> ex <font color="Olive" title="b2">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Olive" title="b2">k1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font> being   <a href="ami_3.html#NM1" title="AMI_3:NM.1">Data-Location</a>, <font color="Maroon" title="c5">k1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:42_1_1_2_9"/><span class="lab"><font color="Green" title="E17">A24</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="ami_3.html#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Maroon" title="c5">k1</font>
 ;<br/><a NAME="E4:42_1_1_2_9"/><span class="lab"><font color="Green" title="E18">A25</font></span>: 
 <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">I</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="c5">k1</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="#E3:42_1_1_2_9"><span class="lab"><font color="Green" title="E17">A24</font></span></a></span>;<br/><a NAME="E5:42_1_1_2_9"/><span class="kw">then </span>
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="finseq_1.html#T90" onmouseover="rs('finseq_1/T90')" onmouseout="rh()">FINSEQ_1:90</a></span>;<br/><a NAME="E6:42_1_1_2_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A26</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1_2_9"><span class="lab"><font color="Green" title="E18">A25</font></span></a>, <a class="txt" href="#E5:42_1_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a></span>;<br/><a NAME="E7:42_1_1_2_9"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</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"><font color="Maroon" title="c5">k1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42_1_1_2_9"><span class="lab"><font color="Green" title="E17">A24</font></span></a>, <a class="ref" href="ami_6.html#T20" target="_self" onmouseover="rs('ami_6/T20')" onmouseout="rh()">Th20</a></span>;<br/><span class="kw">hence </span><a NAME="E8:42_1_1_2_9"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:42_1_1_2_9"><span class="lab"><font color="Green" title="E19">A26</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
