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

<b>let </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">Y</font>;<br/>

<b>given </b><font color="Maroon" title="c8">G1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font><b> such that </b><a NAME="E2:29_1_2"/><i><font color="Green" title="E20">A51</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">G1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">B</font>
 <b>and </b><br/><a NAME="E3:29_1_2"/><i><font color="Green" title="E21">A52</font></i>: 
for <font color="Olive" title="b1">e</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">Y</font>  st <font color="Olive" title="b1">e</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c3">F</font> holds <br/><font color="Maroon" title="c8">G1</font> <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 href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e</font>
 <b>and </b><br/><a NAME="E4:29_1_2"/><i><font color="Green" title="E22">A53</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Maroon" title="c8">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 <b>and </b><br/><a NAME="E5:29_1_2"/><i><font color="Green" title="E23">A54</font></i>: 
for <font color="Olive" title="b1">B'</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">B'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Olive" title="b1">B'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>for <font color="Olive" title="b2">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font> <a href="setwiseo.html#K6" title="SETWISEO:func.6">\</a> <font color="Olive" title="b1">B'</font> holds <br/><font color="Maroon" title="c8">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">G1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">B'</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font></span>)</span>
 ;<br/>

<b>given </b><font color="Maroon" title="c9">G2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font><b> such that </b><a NAME="E7:29_1_2"/><i><font color="Green" title="E24">A55</font></i>: 
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">G2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">B</font>
 <b>and </b><br/><a NAME="E8:29_1_2"/><i><font color="Green" title="E25">A56</font></i>: 
for <font color="Olive" title="b1">e</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">Y</font>  st <font color="Olive" title="b1">e</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c3">F</font> holds <br/><font color="Maroon" title="c9">G2</font> <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 href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e</font>
 <b>and </b><br/><a NAME="E9:29_1_2"/><i><font color="Green" title="E26">A57</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Maroon" title="c9">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 <b>and </b><br/><a NAME="E10:29_1_2"/><i><font color="Green" title="E27">A58</font></i>: 
for <font color="Olive" title="b1">B'</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">B'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Olive" title="b1">B'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>for <font color="Olive" title="b2">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font> <a href="setwiseo.html#K6" title="SETWISEO:func.6">\</a> <font color="Olive" title="b1">B'</font> holds <br/><font color="Maroon" title="c9">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">G2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">B'</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1_2_1"/>
( <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c4">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2_1_1"><b>suppose </b></a><a NAME="E1:29_1_2_1_1"/><i><font color="Green" title="E28">A59</font></i>: 
<font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:29_1_2_1_1"/><b>then </b><i><font color="Green" title="E29">A60</font></i>: 
 <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c3">F</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c3">F</font>
 <b>by </b><i><a class="txt" href="setwiseo.html#E1:29"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="setwiseo.html#T22" target="_self" title="SETWISEO:th.22">Th22</a></i>;<br/><b>hence </b><font color="Maroon" title="c6">x</font> = 
 <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c3">F</font>
<b>by </b><i><a class="txt" href="setwiseo.html#E2:29_1_2"><i><font color="Green" title="E20">A51</font></i></a>, <a class="txt" href="setwiseo.html#E3:29_1_2"><i><font color="Green" title="E21">A52</font></i></a>, <a class="txt" href="setwiseo.html#E1:29_1_2_1_1"><i><font color="Green" title="E28">A59</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c7">y</font>
<b>by </b><i><a class="txt" href="setwiseo.html#E7:29_1_2"><i><font color="Green" title="E24">A55</font></i></a>, <a class="txt" href="setwiseo.html#E8:29_1_2"><i><font color="Green" title="E25">A56</font></i></a>, <a class="txt" href="setwiseo.html#E1:29_1_2_1_1"><i><font color="Green" title="E28">A59</font></i></a>, <a class="txt" href="setwiseo.html#E2:29_1_2_1_1"><i><font color="Green" title="E29">A60</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2_1_2"><b>suppose </b></a><a NAME="E1:29_1_2_1_2"/><i><font color="Green" title="E28">A61</font></i>: 
<font color="Maroon" title="c4">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>( $1 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> &amp; $1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c8">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1 );<br/><a NAME="E2:29_1_2_1_2"/><i><font color="Green" title="E29">A62</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="setwiseo.html#K1" title="SETWISEO:func.1">{}.</a> <font color="Maroon" title="c1">X</font>]
 ;<br/><a NAME="E3:29_1_2_1_2"/><i><font color="Green" title="E30">A63</font></i>: 
for <font color="Olive" title="b1">B'</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">B'</font>] &amp; not <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">B'</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">B'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b2">b</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_2_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">B'</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c11">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><a NAME="E1:29_1_2_1_2_1"/><i><font color="Green" title="E31">A64</font></i>: 
( <font color="Maroon" title="c10">B'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c10">B'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c8">G1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">B'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">G2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">B'</font> )
 ;<br/>

<b>assume </b><a NAME="E2:29_1_2_1_2_1"/><i><font color="Green" title="E32">A65</font></i>: 
not <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">B'</font>
 ;<br/>

<b>assume </b><a NAME="E3:29_1_2_1_2_1"/>
<font color="Maroon" title="c10">B'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c11">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font>
 ;<br/>

<a NAME="E4:29_1_2_1_2_1"/><b>then </b><i><font color="Green" title="E33">A66</font></i>: 
( <font color="Maroon" title="c10">B'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font> )
 
<b>by </b><i><a class="ref" href="setwiseo.html#T8" target="_self" title="SETWISEO:th.8">Th8</a></i>;<br/>
<a NAME="E5:29_1_2_1_2_1"/><b>then </b><i><font color="Green" title="E34">A67</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font> <a href="setwiseo.html#K6" title="SETWISEO:func.6">\</a> <font color="Maroon" title="c10">B'</font>
 
<b>by </b><i><a class="txt" href="setwiseo.html#E2:29_1_2_1_2_1"><i><font color="Green" title="E32">A65</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>assume </b><a NAME="E6:29_1_2_1_2_1"/>
<font color="Maroon" title="c10">B'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c11">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1_2_1_2_1_1"/>
( <font color="Maroon" title="c10">B'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c10">B'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:29_1_2_1_2_1_1_1"/><i><font color="Green" title="E35">A68</font></i>: 
<font color="Maroon" title="c10">B'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c8">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">B'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c11">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> = 
<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font>
<b>by </b><i><a class="txt" href="setwiseo.html#E4:29_1_2"><i><font color="Green" title="E22">A53</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">B'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c11">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="setwiseo.html#E9:29_1_2"><i><font color="Green" title="E26">A57</font></i></a>, <a class="txt" href="setwiseo.html#E1:29_1_2_1_2_1_1_1"><i><font color="Green" title="E35">A68</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:29_1_2_1_2_1_1_2"/><i><font color="Green" title="E35">A69</font></i>: 
<font color="Maroon" title="c10">B'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c8">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">B'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c11">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> = 
<font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">G1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">B'</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font></span>)</span>
<b>by </b><i><a class="txt" href="setwiseo.html#E5:29_1_2"><i><font color="Green" title="E23">A54</font></i></a>, <a class="txt" href="setwiseo.html#E4:29_1_2_1_2_1"><i><font color="Green" title="E33">A66</font></i></a>, <a class="txt" href="setwiseo.html#E5:29_1_2_1_2_1"><i><font color="Green" title="E34">A67</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">B'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c11">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="setwiseo.html#E10:29_1_2"><i><font color="Green" title="E27">A58</font></i></a>, <a class="txt" href="setwiseo.html#E1:29_1_2_1_2_1"><i><font color="Green" title="E31">A64</font></i></a>, <a class="txt" href="setwiseo.html#E4:29_1_2_1_2_1"><i><font color="Green" title="E33">A66</font></i></a>, <a class="txt" href="setwiseo.html#E5:29_1_2_1_2_1"><i><font color="Green" title="E34">A67</font></i></a>, <a class="txt" href="setwiseo.html#E1:29_1_2_1_2_1_1_2"><i><font color="Green" title="E35">A69</font></i></a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E4:29_1_2_1_2"/>
for <font color="Olive" title="b1">B'</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">X</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">B'</font>]
 <b>from </b><i><a class="ref" href="setwiseo.html#S2" target="_self" title="SETWISEO:sch.2">SETWISEO:sch 2</a>(<a class="txt" href="setwiseo.html#E2:29_1_2_1_2"><i><font color="Green" title="E29">A62</font></i></a>, <a class="txt" href="setwiseo.html#E3:29_1_2_1_2"><i><font color="Green" title="E30">A63</font></i></a>);<br/></i><b>hence </b><a NAME="E5:29_1_2_1_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">y</font>
 <b>by </b><i><a class="txt" href="setwiseo.html#E2:29_1_2"><i><font color="Green" title="E20">A51</font></i></a>, <a class="txt" href="setwiseo.html#E7:29_1_2"><i><font color="Green" title="E24">A55</font></i></a>, <a class="txt" href="setwiseo.html#E1:29_1_2_1_2"><i><font color="Green" title="E28">A61</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
