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

<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a> <a href="ami_1.html#V14" title="AMI_1:attr.14">standard-ins</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a> <a href="amistd_2.html#V6" title="AMISTD_2:attr.6">regular</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">F</font>, <font color="Olive" title="b3">G</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="amistd_1.html#V9" title="AMISTD_1:attr.9">lower</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b1">S</font> holds   <a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Olive" title="b2">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Olive" title="b3">G</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a> <a href="ami_1.html#V14" title="AMI_1:attr.14">standard-ins</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a> <a href="amistd_2.html#V6" title="AMISTD_2:attr.6">regular</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">G</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="amistd_1.html#V9" title="AMISTD_1:attr.9">lower</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c2">S</font> holds   <a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Olive" title="b1">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Olive" title="b2">G</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">F</font>, <font color="Maroon" title="c4">G</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="amistd_1.html#V9" title="AMISTD_1:attr.9">lower</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span><br/>





<b>set </b><font color="Maroon" title="c5">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/>
<b>set </b><font color="Maroon" title="c6">P</font> = <font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font>;<br/>
<a NAME="E1:120"/><i><font color="Green" title="E59">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</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="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">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="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">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>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E2:120"/><i><font color="Green" title="E60">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">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"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">m</font></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="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="amistd_2.html#T15" target="_self" title="AMISTD_2:th.15">Th15</a></i>;<br/>
<i><font color="Green" title="E61">A3</font></i>:  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#T49" target="_self" title="AMISTD_2:th.49">Th49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self" title="AMISTD_2:th.52">Th52</a></i>
<br/>.= 
<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="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0: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="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>

;<br/>
<a NAME="E4:120"/><i><font color="Green" title="E62">A4</font></i>: 
for <font color="Olive" title="b1">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>   st <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> holds <br/><font color="Olive" title="b1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">m</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> implies <font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:120_2"/><i><font color="Green" title="E63">A5</font></i>: 
<font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:120_2"/><i><font color="Green" title="E64">A6</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<b>by </b><i><a class="ref" href="amistd_2.html#T49" target="_self" title="AMISTD_2:th.49">Th49</a></i>;<br/>
<a NAME="E3:120_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></i>;<br/>
<a NAME="E4:120_2"/><b>then </b>
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/>
<a NAME="E5:120_2"/><b>then </b>
<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="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0: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="c4">G</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<b>hence </b><a NAME="E6:120_2"/>
<font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:120"><i><font color="Green" title="E61">A3</font></i></a>, <a class="txt" href="#E1:120_2"><i><font color="Green" title="E63">A5</font></i></a>, <a class="txt" href="#E2:120_2"><i><font color="Green" title="E64">A6</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E5:120"/><i><font color="Green" title="E63">A7</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c7">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="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> or <font color="Maroon" title="c7">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="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:120_3"/>
<font color="Maroon" title="c7">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="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">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="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span><br/>

<b>then consider </b><font color="Maroon" title="c8">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> <b> such that </b><br/><a NAME="E3:120_3"/><i><font color="Green" title="E64">A8</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c8">m</font>
 <b>and </b><br/><a NAME="E4:120_3"/><i><font color="Green" title="E65">A9</font></i>: 
<font color="Maroon" title="c8">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:120"><i><font color="Green" title="E60">A2</font></i></a></i>;<br/>
<a NAME="E5:120_3"/>
<font color="Maroon" title="c8">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E4:120"><i><font color="Green" title="E62">A4</font></i></a>, <a class="txt" href="#E4:120_3"><i><font color="Green" title="E65">A9</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:120_3"/>
<font color="Maroon" title="c7">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="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:120_3"><i><font color="Green" title="E64">A8</font></i></a>, <a class="ref" href="amistd_1.html#T50" title="AMISTD_1:th.50">AMISTD_1:50</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E6:120"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">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="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">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="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">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="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> implies <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">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">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> )</span><br/>

<b>assume </b><a NAME="E1:120_4"/><i><font color="Green" title="E64">A10</font></i>: 
<font color="Maroon" title="c7">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="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">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">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span><br/>

<b>then consider </b><font color="Maroon" title="c8">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> <b> such that </b><br/><a NAME="E3:120_4"/><i><font color="Green" title="E65">A11</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c8">m</font>
 <b>and </b><br/><a NAME="E4:120_4"/><i><font color="Green" title="E66">A12</font></i>: 
<font color="Maroon" title="c8">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:120"><i><font color="Green" title="E60">A2</font></i></a></i>;<br/>
<a NAME="E5:120_4"/><i><font color="Green" title="E67">A13</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">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"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">w</font> <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> where <font color="Olive" title="b1">w</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>  :  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">w</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="amistd_2.html#K8" title="AMISTD_2:func.8">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> 
 
<b>by </b><i><a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>;<br/>
<div><i><font color="Green" title="E68">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="120_4_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:120_4_1"/>
<font color="Maroon" title="c7">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="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><b>then consider </b><font color="Maroon" title="c9">w</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> <b> such that </b><br/><a NAME="E3:120_4_1"/><i><font color="Green" title="E69">A15</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">w</font> <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>
 <b>and </b><br/><a NAME="E4:120_4_1"/>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c9">w</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="amistd_2.html#K8" title="AMISTD_2:func.8">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>
 <b>by </b><i><a class="txt" href="#E5:120_4"><i><font color="Green" title="E67">A13</font></i></a></i>;<br/><a NAME="E5:120_4_1"/>
<font color="Maroon" title="c8">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <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="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="#E4:120_4"><i><font color="Green" title="E66">A12</font></i></a>, <a class="ref" href="amistd_2.html#T49" target="_self" title="AMISTD_2:th.49">Th49</a></i>;<br/><a NAME="E6:120_4_1"/><b>then </b><i><font color="Green" title="E70">A16</font></i>: 
<font color="Maroon" title="c8">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <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
 <b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>;<br/><a NAME="E7:120_4_1"/>
<font color="Maroon" title="c8">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w</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>
 <b>by </b><i><a class="txt" href="#E3:120_4"><i><font color="Green" title="E65">A11</font></i></a>, <a class="txt" href="#E3:120_4_1"><i><font color="Green" title="E69">A15</font></i></a>, <a class="ref" href="amistd_1.html#T25" title="AMISTD_1:th.25">AMISTD_1:25</a></i>;<br/><b>hence </b><a NAME="E8:120_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E6:120_4_1"><i><font color="Green" title="E70">A16</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E7:120_4"/><i><font color="Green" title="E69">A17</font></i>: 
<font color="Maroon" title="c7">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"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:120"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="#E1:120_4"><i><font color="Green" title="E64">A10</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:120_4_2"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:120_4_2"/><b>then </b>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c8">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<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> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="#E3:120_4"><i><font color="Green" title="E65">A11</font></i></a>, <a class="ref" href="amistd_1.html#T55" title="AMISTD_1:th.55">AMISTD_1:55</a></i>;<br/><b>then </b><i><font color="Green" title="E70">A18</font></i>: <font color="Maroon" title="c8">m</font> = 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
<b>by </b><i><a class="ref" href="amistd_1.html#T25" title="AMISTD_1:th.25">AMISTD_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="ref" href="pre_circ.html#T25" title="PRE_CIRC:th.25">PRE_CIRC:25</a></i>
;<br/><a NAME="E4:120_4_2"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="amistd_2.html#T49" target="_self" title="AMISTD_2:th.49">Th49</a></i>;<br/><b>hence </b><a NAME="E5:120_4_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:120"><i><font color="Green" title="E62">A4</font></i></a>, <a class="txt" href="#E4:120_4"><i><font color="Green" title="E66">A12</font></i></a>, <a class="txt" href="#E3:120_4_2"><i><font color="Green" title="E70">A18</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E9:120_4"/><b>then </b>
not <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E10:120_4"/><b>then </b>
not <font color="Maroon" title="c7">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"><span class="p2">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></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"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E11:120_4"/><b>then </b>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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"><span class="p3">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></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"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E7:120_4"><i><font color="Green" title="E69">A17</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="ami_1.html#K37" title="AMI_1:func.37">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="ref" href="grfunc_1.html#T93" title="GRFUNC_1:th.93">GRFUNC_1:93</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">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">x</font>
<b>by </b><i><a class="txt" href="#E6:120_4"><i><font color="Green" title="E68">A14</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:120"/>
 <a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_2.html#K10" title="AMISTD_2:func.10">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K11" title="AMISTD_2:func.11">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:120"><i><font color="Green" title="E63">A7</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
