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

<span class="kw">set </span><font color="Maroon" title="c5">P</font> = <font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">k</font> = <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">f</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="amistd_1.html#D9" title="AMISTD_1:def.9">AMISTD_1:def 9</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="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="relset_1.html#K1" title="RELSET_1:func.1">K483</a>(<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>) or  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c7">f</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="relset_1.html#K1" title="RELSET_1:func.1">K483</a>(<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:36_1_1"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c7">f</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="relset_1.html#K1" title="RELSET_1:func.1">K483</a>(<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>)</span><br/>

<a NAME="E2:36_1_1"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p2">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E3:36_1_1"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c3">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>;<br/>
<a NAME="E4:36_1_1"/><span class="lab"><font color="Green" title="E15">A4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span> </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D12" title="VALUED_1:def.12">VALUED_1:def 12</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</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="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c7">f</font>) or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="relset_1.html#K1" title="RELSET_1:func.1">K483</a>(<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>) )</span><br/>

<span class="kw">assume </span><a NAME="E5:36_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c7">f</font>)
 ; <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="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="relset_1.html#K1" title="RELSET_1:func.1">K483</a>(<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>)</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">s2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a>  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E7:36_1_1"/><span class="lab"><font color="Green" title="E16">A5</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c9">s2</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E8:36_1_1"/><span class="lab"><font color="Green" title="E17">A6</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c9">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font>
 ;<br/>
<a NAME="E9:36_1_1"/><span class="lab"><font color="Green" title="E18">A7</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_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="E1:36_1_1_1"/>
( <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> or <font color="Maroon" title="c7">f</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="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E2:36_1_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_1"/><span class="lab"><font color="Green" title="E19">A8</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">F</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="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="relset_1.html#K1" title="RELSET_1:func.1">K483</a>(<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>)</span><br/><div class="add"><a NAME="E2:36_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A9</font></span>: 
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c7">f</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c3">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="amistd_1.html#D9" title="AMISTD_1:def.9">AMISTD_1:def 9</a></span>;<br/><a NAME="E3:36_1_1_1_1"/>
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T36" title="VALUED_1:th.36">VALUED_1:36</a></span>;<br/><a NAME="E4:36_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A10</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c3">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1_1_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E5:36_1_1_1_1"/>
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T18" title="COMPOS_1:th.18">COMPOS_1:18</a></span>;<br/><a NAME="E6:36_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A11</font></span>: 
 not <font color="Maroon" title="c7">f</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="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1_1_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>;<br/><span class="lab"><font color="Green" title="E23">A12</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36_1_1_1_1"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1_1_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1_1_1"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
;<br/><a NAME="E8:36_1_1_1_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c9">s2</font>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c7">f</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36_1_1"><span class="lab"><font color="Green" title="E17">A6</font></span></a></span>;<br/><a NAME="E9:36_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A13</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c3">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:36_1_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E2:36_1_1_1_1"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E7:36_1_1_1_1"><span class="lab"><font color="Green" title="E23">A12</font></span></a></span>;<br/><a NAME="E10:36_1_1_1_1"/>
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T21" title="COMPOS_1:th.21">COMPOS_1:21</a></span>;<br/><span class="kw">hence </span><a NAME="E11:36_1_1_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="relset_1.html#K1" title="RELSET_1:func.1">K483</a>(<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:36_1_1_1_1"><span class="lab"><font color="Green" title="E24">A13</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="36_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_2"/><span class="lab"><font color="Green" title="E19">A14</font></span>: 
<font color="Maroon" title="c7">f</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="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</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="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="relset_1.html#K1" title="RELSET_1:func.1">K483</a>(<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>)</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:36_1_1_1_2"/><span class="lab"><font color="Green" title="E20">A15</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:36_1_1_1_2"/><span class="lab"><font color="Green" title="E21">A16</font></span>: 
<font color="Maroon" title="c10">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a></span>;<br/><a NAME="E5:36_1_1_1_2"/><span class="lab"><font color="Green" title="E22">A17</font></span>: 
<font color="Maroon" title="c10">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c4">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1_1_2"><span class="lab"><font color="Green" title="E21">A16</font></span></a>, <a class="ref" href="compos_1.html#D19" title="COMPOS_1:def.19">COMPOS_1:def 19</a></span>;<br/><a NAME="E6:36_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A18</font></span>: 
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c10">m</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c4">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#D9" title="AMISTD_1:def.9">AMISTD_1:def 9</a></span>;<br/><a NAME="E7:36_1_1_1_2"/><span class="lab"><font color="Green" title="E24">A19</font></span>: 
 <a href="memstr_0.html#K2" title="MEMSTR_0:func.2">ObjectKind</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <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="ref" href="memstr_0.html#D3" title="MEMSTR_0:def.3">MEMSTR_0:def 3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c11">v</font> = <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">m</font> as   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:36_1_1_1_2"><span class="lab"><font color="Green" title="E24">A19</font></span></a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c12">s1</font> = <font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font>;<br/><span class="lab"><font color="Green" title="E25">A20</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">f</font> = 
<span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:36_1_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E1:36_1_1_1_2"><span class="lab"><font color="Green" title="E19">A14</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_1_2"><span class="lab"><font color="Green" title="E20">A15</font></span></a>, <a class="txt" href="#E4:36_1_1_1_2"><span class="lab"><font color="Green" title="E21">A16</font></span></a>, <a class="ref" href="valued_1.html#D12" title="VALUED_1:def.12">VALUED_1:def 12</a></span>
;<br/><a NAME="E10:36_1_1_1_2"/><span class="lab"><font color="Green" title="E26">A21</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>;<br/><a NAME="E11:36_1_1_1_2"/><span class="lab"><font color="Green" title="E27">A22</font></span>: 
 <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <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"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <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="E12:36_1_1_1_2"/><span class="lab"><font color="Green" title="E28">A23</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">m</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"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c13">w</font> = <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> as   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:36_1_1_1_2"><span class="lab"><font color="Green" title="E24">A19</font></span></a></span>;<br/><a NAME="E14:36_1_1_1_2"/><span class="lab"><font color="Green" title="E29">A24</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/><a NAME="E15:36_1_1_1_2"/><span class="lab"><font color="Green" title="E30">A25</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/><a NAME="E16:36_1_1_1_2"/>
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">a</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="c9">s2</font> holds <br/><font color="Maroon" title="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c14">a</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"> ( <font color="Maroon" title="c14">a</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="c9">s2</font> implies <font color="Maroon" title="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:36_1_1_1_2_2"/>
<font color="Maroon" title="c14">a</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="c9">s2</font>
 ; <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="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font></span><br/>

<a NAME="E2:36_1_1_1_2_2"/><span class="lab"><font color="Green" title="E31">A26</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></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"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_2_2_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="E1:36_1_1_1_2_2_1"/>
( <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  or <font color="Maroon" title="c14">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_2_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_2_2_1_1"/><span class="lab"><font color="Green" title="E32">A27</font></span>: 
<font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</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="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> = 
<span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36_1_1"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E3:36_1_1_1_2"><span class="lab"><font color="Green" title="E20">A15</font></span></a>, <a class="txt" href="#E12:36_1_1_1_2"><span class="lab"><font color="Green" title="E28">A23</font></span></a>, <a class="txt" href="#E10:36_1_1_1_2"><span class="lab"><font color="Green" title="E26">A21</font></span></a>, <a class="txt" href="#E11:36_1_1_1_2"><span class="lab"><font color="Green" title="E27">A22</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1_1_2_2_1_1"><span class="lab"><font color="Green" title="E32">A27</font></span></a>, <a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:36_1_1_1_2"><span class="lab"><font color="Green" title="E27">A22</font></span></a>, <a class="txt" href="#E2:36_1_1_1_2_2"><span class="lab"><font color="Green" title="E31">A26</font></span></a>, <a class="txt" href="#E1:36_1_1_1_2_2_1_1"><span class="lab"><font color="Green" title="E32">A27</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
;<br/> <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="36_1_1_1_2_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_2_2_1_2"/><span class="lab"><font color="Green" title="E32">A28</font></span>: 
<font color="Maroon" title="c14">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</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="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font></span><br/><div class="add"><a NAME="E2:36_1_1_1_2_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A29</font></span>: 
 not <font color="Maroon" title="c14">a</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"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1_1_1_2_2"><span class="lab"><font color="Green" title="E31">A26</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E3:36_1_1_1_2_2_1_2"/>
 not <font color="Maroon" title="c14">a</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"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">m</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:36_1_1_1_2"><span class="lab"><font color="Green" title="E28">A23</font></span></a>, <a class="txt" href="#E1:36_1_1_1_2_2_1_2"><span class="lab"><font color="Green" title="E32">A28</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E4:36_1_1_1_2_2_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>;<br/><span class="kw">hence </span><a NAME="E5:36_1_1_1_2_2_1_2"/>
<font color="Maroon" title="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1_1_1_2_2_1_2"><span class="lab"><font color="Green" title="E33">A29</font></span></a>, <a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div><a NAME="E17:36_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A30</font></span>: 
<font color="Maroon" title="c9">s2</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:36_1_1_1_2"><span class="lab"><font color="Green" title="E29">A24</font></span></a>, <a class="txt" href="#E15:36_1_1_1_2"><span class="lab"><font color="Green" title="E30">A25</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c14">s3</font> = <font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font>;<br/><span class="lab"><font color="Green" title="E32">A32</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>

<br/>.= 
<font color="Maroon" title="c10">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:36_1_1_1_2"><span class="lab"><font color="Green" title="E26">A21</font></span></a>, <a class="txt" href="#E11:36_1_1_1_2"><span class="lab"><font color="Green" title="E27">A22</font></span></a>, <a class="txt" href="#E12:36_1_1_1_2"><span class="lab"><font color="Green" title="E28">A23</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
;<br/><span class="kw">reconsider </span><font color="Maroon" title="c15">s3</font> = <font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a>  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#T107" title="CARD_3:th.107">CARD_3:107</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c16">k</font> = <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1, <font color="Maroon" title="c17">m</font> = <font color="Maroon" title="c10">m</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/><span class="lab"><font color="Green" title="E33">A37</font></span>: <font color="Maroon" title="c8">x</font> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span>,<font color="Maroon" title="c16">k</font>)</span>)</span>,<font color="Maroon" title="c9">s2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:36_1_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E5:36_1_1_1_2"><span class="lab"><font color="Green" title="E22">A17</font></span></a>, <a class="txt" href="#E9:36_1_1_1_2"><span class="lab"><font color="Green" title="E25">A20</font></span></a>, <a class="ref" href="compos_1.html#D19" title="COMPOS_1:def.19">COMPOS_1:def 19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">v</font></span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c16">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:36_1_1_1_2"><span class="lab"><font color="Green" title="E31">A30</font></span></a>, <a class="ref" href="amistd_2.html#T7" target="_self" title="AMISTD_2:th.7">Th47</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span>,<font color="Maroon" title="c15">s3</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c16">k</font>

;<br/><a NAME="E22:36_1_1_1_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span>,<font color="Maroon" title="c15">s3</font>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span>,<font color="Maroon" title="c17">m</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:36_1_1_1_2"><span class="lab"><font color="Green" title="E32">A32</font></span></a></span>;<br/><a NAME="E23:36_1_1_1_2"/><span class="kw">then </span>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span>,<font color="Maroon" title="c15">s3</font>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c4">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36_1_1_1_2"><span class="lab"><font color="Green" title="E23">A18</font></span></a></span>;<br/><a NAME="E24:36_1_1_1_2"/><span class="kw">then </span>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c17">m</font></span>)</span>,<font color="Maroon" title="c15">s3</font>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c16">k</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D19" title="COMPOS_1:def.19">COMPOS_1:def 19</a></span>;<br/><a NAME="E25:36_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">x</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="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c16">k</font>)</span>)</span>,<font color="Maroon" title="c16">k</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E21:36_1_1_1_2"><span class="lab"><font color="Green" title="E33">A37</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E26:36_1_1_1_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="relset_1.html#K1" title="RELSET_1:func.1">K483</a>(<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="compos_1.html#K12" title="COMPOS_1:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
