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

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">U</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b2">l</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b3">I</font> being  <font color="Maroon" title="c1">S</font>,<font color="Olive">b<sub>1</sub></font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  ex <font color="Olive" title="b4">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">U</font> st <br/>( <font color="Olive" title="b4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Olive" title="b2">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> &amp; (<font color="Olive" title="b2">l</font>,<font color="Olive" title="b4">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">I</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">U</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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">  for <font color="Olive" title="b1">l</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">I</font> being  <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  ex <font color="Olive" title="b3">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">U</font> st <br/>( <font color="Olive" title="b3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Olive" title="b1">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> &amp; (<font color="Olive" title="b1">l</font>,<font color="Olive" title="b3">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">I</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">l</font> be   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being  <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  ex <font color="Olive" title="b2">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">U</font> st <br/>( <font color="Olive" title="b2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> &amp; (<font color="Maroon" title="c3">l</font>,<font color="Olive" title="b2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">I</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">I</font> be  <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">U</font> st <br/>( <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> &amp; (<font color="Maroon" title="c3">l</font>,<font color="Olive" title="b1">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">I</font> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">O</font> =  <a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<a NAME="E1:201"/>
<span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<a NAME="E2:201"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">B0</font></span>: 
(  <a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">I</font> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">lo</font> = <font color="Maroon" title="c3">l</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D19" title="FOMODEL1:def.19">FOMODEL1:def 19</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">i</font> = <font color="Maroon" title="c4">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Maroon" title="c3">l</font> as    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">U</font> ;<br/>
<a NAME="E5:201"/>
( <font color="Maroon" title="c7">i</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c2">U</font></span>)</span>,<font color="Maroon" title="c2">U</font> &amp; <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c2">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D2" target="_self" title="FOMODEL2:def.2">DefInterpreter1</a>, <a class="ref" href="fomodel0.html#T10" title="FOMODEL0:th.10">FOMODEL0:10</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">ii</font> = <font color="Maroon" title="c7">i</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">U</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">e</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">u</font> = <font color="Maroon" title="c8">ii</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">e</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">U</font> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c10">u</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="c10">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> &amp; (<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c10">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">I</font> )</span><br/>

<span class="kw">thus </span><a NAME="E9:201"/>
<font color="Maroon" title="c10">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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="c3">l</font>,<font color="Maroon" title="c10">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">I</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c11">h</font> = <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">H</font> = <font color="Maroon" title="c3">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">J</font> = (<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c10">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c4">I</font>;<br/>
<a NAME="E10:201"/>
<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c10">u</font>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">hh</font> = <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">U</font> ;<br/>
<a NAME="E12:201"/><span class="lab"><font color="Green" title="E84">B2</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c6">lo</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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/>
<a NAME="E13:201"/><span class="kw">then </span><span class="lab"><font color="Green" title="E85">B1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font></span>)</span></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> <font color="Maroon" title="c4">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:201"><span class="lab"><font color="Green" title="E83">B0</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="201_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c15">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>; <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">ii</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">hh</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">z</font></span><br/><a NAME="E1:201_1"/>
( <font color="Maroon" title="c8">ii</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">u</font> &amp; <font color="Maroon" title="c14">hh</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" title="FUNCOP_1:th.7">FUNCOP_1:7</a></span>;<br/><span class="kw">hence </span><a NAME="E2:201_1"/>
<font color="Maroon" title="c8">ii</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">hh</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E15:201"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">B3</font></span>: 
<font color="Maroon" title="c8">ii</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">hh</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" title="FUNCT_2:th.63">FUNCT_2:63</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="201_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c15">z</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="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">z</font> )</span><br/><span class="kw">assume </span><a NAME="E1:201_2"/>
<font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font></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"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">z</font></span><br/><a NAME="E2:201_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">C0</font></span>: 
<font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">l</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">z</font> = 
<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" title="FUNCOP_1:th.7">FUNCOP_1:7</a></span>
<br/>.= 
<font color="Maroon" title="c4">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">z</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:201"><span class="lab"><font color="Green" title="E86">B3</font></span></a>, <a class="txt" href="#E2:201_2"><span class="lab"><font color="Green" title="E87">C0</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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>
<a NAME="E17:201"/><span class="kw">then </span>
<font color="Maroon" title="c3">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c4">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:201"><span class="lab"><font color="Green" title="E85">B1</font></span></a>, <a class="ref" href="partfun1.html#T53" title="PARTFUN1:th.53">PARTFUN1:53</a></span>;<br/>
<span class="kw">then </span>(<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c10">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c4">I</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c10">u</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T34" title="FUNCT_4:th.34">FUNCT_4:34</a></span>
<br/>.= 
<font color="Maroon" title="c4">I</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:201"><span class="lab"><font color="Green" title="E84">B2</font></span></a>, <a class="txt" href="#E2:201"><span class="lab"><font color="Green" title="E83">B0</font></span></a>, <a class="ref" href="funct_4.html#T19" title="FUNCT_4:th.19">FUNCT_4:19</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E19:201"/>
(<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c10">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">I</font>
 ; <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>
