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

<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">PA1</font>, <font color="Maroon" title="c3">PA2</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">A</font>;<br/>





<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <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> $2;<br/>
<b>assume </b><a NAME="E1:11"/><i><font color="Green" title="E9">A1</font></i>: 
( <font color="Maroon" title="c2">PA1</font> <a href="setfam_1.html#R1" title="SETFAM_1:pred.1">is_finer_than</a> <font color="Maroon" title="c3">PA2</font> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">PA1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">PA2</font> )
 ;<br/>

<a NAME="E2:11"/><b>then </b><i><font color="Green" title="E10">A2</font></i>: 
for <font color="Olive" title="b1">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">PA1</font> holds <br/> ex <font color="Olive" title="b2">u</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">PA2</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">e</font>,<font color="Olive" title="b2">u</font>] )
 
<b>by </b><i><a class="ref" href="setfam_1.html#D2" title="SETFAM_1:def.2">SETFAM_1:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">PA1</font>,<font color="Maroon" title="c3">PA2</font><b> such that </b><br/><a NAME="E4:11"/><i><font color="Green" title="E11">A3</font></i>: 
for <font color="Olive" title="b1">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">PA1</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S1" title="FUNCT_2:sch.1">FUNCT_2:sch 1</a>(<a class="txt" href="fsm_1.html#E2:11"><i><font color="Green" title="E10">A2</font></i></a>);<br/></i>
<a NAME="E5:11"/><i><font color="Green" title="E12">A4</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">PA1</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">PA2</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/>
<a NAME="E6:11"/><i><font color="Green" title="E13">A5</font></i>: 
<font color="Maroon" title="c3">PA2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">f</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">p2</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><br/>

<b>assume </b><a NAME="E1:11_1"/>
<font color="Maroon" title="c5">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">PA2</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c6">p2'</font> = <font color="Maroon" title="c5">p2</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">PA2</font> ;<br/>
<b>consider </b><font color="Maroon" title="c7">p1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">PA1</font><b> such that </b><br/><a NAME="E4:11_1"/><i><font color="Green" title="E14">A6</font></i>: 
<font color="Maroon" title="c7">p1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">p2'</font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:11"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="fsm_1.html#T14" target="_self" title="FSM_1:th.14">Th14</a></i>;<br/>
<a NAME="E5:11_1"/><i><font color="Green" title="E15">A7</font></i>: 
<font color="Maroon" title="c7">p1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p1</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E4:11"><i><font color="Green" title="E11">A3</font></i></a></i>;<br/>
<a NAME="E6:11_1"/><i><font color="Green" title="E16">A8</font></i>: 
<font color="Maroon" title="c6">p2'</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c8">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E2:11_1_1"/><i><font color="Green" title="E17">A9</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">p1</font>
 <b>by </b><i><a class="ref" href="fsm_1.html#T11" target="_self" title="FSM_1:th.11">Th11</a></i>;<br/>
<b>thus </b><a NAME="E3:11_1_1"/>
<font color="Maroon" title="c6">p2'</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p1</font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:11_1"><i><font color="Green" title="E14">A6</font></i></a>, <a class="txt" href="fsm_1.html#E5:11_1"><i><font color="Green" title="E15">A7</font></i></a>, <a class="txt" href="fsm_1.html#E2:11_1_1"><i><font color="Green" title="E17">A9</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>


</div><b>end;</b></div>
<b>reconsider </b><font color="Maroon" title="c8">fp1</font> = <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E8:11_1"/>
<font color="Maroon" title="c6">p2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">fp1</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E6:11_1"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="eqrel_1.html#D6" title="EQREL_1:def.6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E9:11_1"/>
<font color="Maroon" title="c5">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:11"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:11"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">PA2</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E5:11"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E8:11"/><b>then </b><i><font color="Green" title="E14">A10</font></i>: 
<font color="Maroon" title="c4">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E1:11"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="finseq_4.html#T79" title="FINSEQ_4:th.79">FINSEQ_4:79</a></i>;<br/>
<a NAME="E9:11"/><i><font color="Green" title="E15">A11</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">PA1</font> holds  <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">PA1</font>;<br/>

<a NAME="E1:11_2"/><i><font color="Green" title="E16">A12</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E4:11"><i><font color="Green" title="E11">A3</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">fx</font> = <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E3:11_2"/><i><font color="Green" title="E17">A13</font></i>: 
<font color="Maroon" title="c6">fx</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 
;<br/>
<b>assume </b><a NAME="E4:11_2"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c7">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:11_2"/><i><font color="Green" title="E18">A14</font></i>: 
( ( <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">x</font> &amp; not <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> ) or ( <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> &amp; not <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">x</font> ) )
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">E1</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E8:11_2"/><i><font color="Green" title="E19">A15</font></i>: 
<font color="Maroon" title="c2">PA1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon" title="c8">E1</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T43" title="EQREL_1:th.43">EQREL_1:43</a></i>;<br/>
<a NAME="E9:11_2"/><i><font color="Green" title="E20">A16</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c8">E1</font>,<font color="Maroon" title="c7">a</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E3:11_2"><i><font color="Green" title="E17">A13</font></i></a>, <a class="txt" href="fsm_1.html#E6:11_2"><i><font color="Green" title="E18">A14</font></i></a>, <a class="ref" href="eqrel_1.html#T28" title="EQREL_1:th.28">EQREL_1:28</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">CE1a</font> =  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c8">E1</font>,<font color="Maroon" title="c7">a</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">PA1</font> <b>by </b><i><a class="txt" href="fsm_1.html#E3:11_2"><i><font color="Green" title="E17">A13</font></i></a>, <a class="txt" href="fsm_1.html#E6:11_2"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="fsm_1.html#E8:11_2"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/>
<a NAME="E11:11_2"/><i><font color="Green" title="E21">A17</font></i>: 
<font color="Maroon" title="c9">CE1a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">CE1a</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E4:11"><i><font color="Green" title="E11">A3</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">fCE1a</font> = <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">CE1a</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E13:11_2"/>
<font color="Maroon" title="c6">fx</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c10">fCE1a</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E1:11_2"><i><font color="Green" title="E16">A12</font></i></a>, <a class="txt" href="fsm_1.html#E6:11_2"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="fsm_1.html#E9:11_2"><i><font color="Green" title="E20">A16</font></i></a>, <a class="txt" href="fsm_1.html#E11:11_2"><i><font color="Green" title="E21">A17</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E14:11_2"/><b>then </b>
<font color="Maroon" title="c6">fx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">fCE1a</font>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D6" title="EQREL_1:def.6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E15:11_2"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:11"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="fsm_1.html#E8:11"><i><font color="Green" title="E14">A10</font></i></a>, <a class="txt" href="fsm_1.html#E1:11_2"><i><font color="Green" title="E16">A12</font></i></a>, <a class="txt" href="fsm_1.html#E6:11_2"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="fsm_1.html#E9:11_2"><i><font color="Green" title="E20">A16</font></i></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:11_3_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">PA1</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c6">x'</font> = <font color="Maroon" title="c5">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">PA1</font> ;<br/><b>set </b><font color="Maroon" title="c7">fx</font> = <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x'</font>;<br/><a NAME="E3:11_3_1"/>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">PA2</font>
 ;<br/><b>hence </b><a NAME="E4:11_3_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">PA2</font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E9:11"><i><font color="Green" title="E15">A11</font></i></a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:11_3"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">PA2</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:11_3"/><i><font color="Green" title="E16">A18</font></i>: 
( <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:11"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c7">y'</font> = <font color="Maroon" title="c6">y</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">PA1</font> <b>by </b><i><a class="txt" href="fsm_1.html#E4:11_3"><i><font color="Green" title="E16">A18</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E6:11_3"/>
<font color="Maroon" title="c7">y'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">y'</font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E9:11"><i><font color="Green" title="E15">A11</font></i></a></i>;<br/><b>hence </b><a NAME="E7:11_3"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">PA1</font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:11_3"><i><font color="Green" title="E16">A18</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:11"/>
<font color="Maroon" title="c2">PA1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">PA2</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


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