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

<b>let </b><font color="Maroon" title="c6">F1</font>, <font color="Maroon" title="c7">F2</font> be  <a href="cohsp_1.html#V6" title="COHSP_1:attr.6">V202</a> <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font>, <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</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">H</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c6">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K62" title="MODELC_1:func.62">SigFoaxTau</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c4">f</font>,<font color="Olive" title="b1">H</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font> ) &amp; ( for <font color="Olive" title="b1">H</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c7">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K62" title="MODELC_1:func.62">SigFoaxTau</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c4">f</font>,<font color="Olive" title="b1">H</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font> ) implies <font color="Maroon" title="c6">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:177_1_2"/><i><font color="Green" title="E133">A6</font></i>: 
for <font color="Olive" title="b1">H</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c6">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K62" title="MODELC_1:func.62">SigFoaxTau</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c4">f</font>,<font color="Olive" title="b1">H</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>
 <b>and </b><br/><a NAME="E2:177_1_2"/><i><font color="Green" title="E134">A7</font></i>: 
for <font color="Olive" title="b1">H</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c7">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K62" title="MODELC_1:func.62">SigFoaxTau</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c4">f</font>,<font color="Olive" title="b1">H</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font></span><br/>

<a NAME="E3:177_1_2"/>
for <font color="Olive" title="b1">H</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font> holds <br/><font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="177_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">H</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="c8">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font> implies <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">H</font> )</span><br/>

<b>assume </b><a NAME="E1:177_1_2_1"/><i><font color="Green" title="E135">A8</font></i>: 
<font color="Maroon" title="c8">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">H</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c9">H</font> = <font color="Maroon" title="c8">H</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> <b>by </b><i><a class="txt" href="modelc_1.html#E1:177_1_2_1"><i><font color="Green" title="E135">A8</font></i></a></i>;<br/>
<font color="Maroon" title="c6">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">H</font> = 
 <a href="modelc_1.html#K62" title="MODELC_1:func.62">SigFoaxTau</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c9">H</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E1:177_1_2"><i><font color="Green" title="E133">A6</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">H</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E2:177_1_2"><i><font color="Green" title="E134">A7</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E4:177_1_2_1"/>
<font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">H</font>
 ; <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="E4:177_1_2"/>
<font color="Maroon" title="c6">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</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>
