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

<b>let </b><font color="Maroon" title="c1">g1</font>, <font color="Maroon" title="c2">g2</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="c1">g1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon">F<sub>1</sub></font>() &amp; ( for <font color="Olive" title="b1">s</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>( <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s</font>,<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) ) &amp; <font color="Maroon" title="c2">g2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon">F<sub>1</sub></font>() &amp; ( for <font color="Olive" title="b1">s</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>( <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s</font>,<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) ) implies <font color="Maroon" title="c1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:88_1"/><i><font color="Green" title="E71">A1</font></i>: 
<font color="Maroon" title="c1">g1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E2:88_1"/><i><font color="Green" title="E72">A2</font></i>: 
for <font color="Olive" title="b1">s</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>( <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s</font>,<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 <b>and </b><br/><a NAME="E3:88_1"/><i><font color="Green" title="E73">A3</font></i>: 
<font color="Maroon" title="c2">g2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E4:88_1"/><i><font color="Green" title="E74">A4</font></i>: 
for <font color="Olive" title="b1">s</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>( <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s</font>,<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g2</font></span><br/>

<a NAME="E5:88_1"/><i><font color="Green" title="E75">A5</font></i>: 
for <font color="Olive" title="b1">s</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="88_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">s</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="c3">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() implies <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font> )</span><br/>

<b>assume </b><a NAME="E1:88_1_1"/><i><font color="Green" title="E76">A6</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 ; <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="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font></span><br/>

<b>set </b><font color="Maroon" title="c4">F1</font> = <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c3">s</font>,<font color="Maroon">F<sub>2</sub></font>());<br/>
<b>set </b><font color="Maroon" title="c5">f1</font> = <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font>;<br/>
<b>set </b><font color="Maroon" title="c6">f2</font> = <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font>;<br/>
<a NAME="E2:88_1_1"/><i><font color="Green" title="E77">A7</font></i>: 
( <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c3">s</font>,<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 
<b>by </b><i><a class="txt" href="#E2:88_1"><i><font color="Green" title="E72">A2</font></i></a>, <a class="txt" href="#E1:88_1_1"><i><font color="Green" title="E76">A6</font></i></a></i>;<br/>
<a NAME="E3:88_1_1"/><i><font color="Green" title="E78">A8</font></i>: 
( <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c3">s</font>,<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 
<b>by </b><i><a class="txt" href="#E4:88_1"><i><font color="Green" title="E74">A4</font></i></a>, <a class="txt" href="#E1:88_1_1"><i><font color="Green" title="E76">A6</font></i></a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="88_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:88_1_1_1"/>
( <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c3">s</font>,<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  or <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c3">s</font>,<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="88_1_1_1_1"><b>suppose </b></a><a NAME="E1:88_1_1_1_1"/>
<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c3">s</font>,<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ; <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="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font></span><br/><div class="add"><b>hence </b><a NAME="E2:88_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font>
 <b>by </b><i><a class="txt" href="#E4:88_1"><i><font color="Green" title="E74">A4</font></i></a>, <a class="txt" href="#E1:88_1_1"><i><font color="Green" title="E76">A6</font></i></a>, <a class="txt" href="#E2:88_1_1"><i><font color="Green" title="E77">A7</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="88_1_1_1_2"><b>suppose </b></a><a NAME="E1:88_1_1_1_2"/><i><font color="Green" title="E79">A9</font></i>: 
<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c3">s</font>,<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ; <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="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font></span><br/><div class="add"><a NAME="E2:88_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <b>by </b><i><a class="txt" href="#E1:88_1_1"><i><font color="Green" title="E76">A6</font></i></a>, <a class="txt" href="#E2:88_1_1"><i><font color="Green" title="E77">A7</font></i></a>, <a class="txt" href="modelc_1.html#E86"><i><font color="Green" title="E70">Lm35</font></i></a></i>;<br/><b>hence </b><a NAME="E3:88_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">s</font>
 <b>by </b><i><a class="txt" href="#E1:88_1_1"><i><font color="Green" title="E76">A6</font></i></a>, <a class="txt" href="#E3:88_1_1"><i><font color="Green" title="E78">A8</font></i></a>, <a class="txt" href="#E1:88_1_1_1_2"><i><font color="Green" title="E79">A9</font></i></a>, <a class="txt" href="modelc_1.html#E86"><i><font color="Green" title="E70">Lm35</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></div><b>end;</b></div>

</div><b>end;</b></div>
<font color="Maroon" title="c1">g1</font> = 
 <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c1">g1</font>,<font color="Maroon">F<sub>1</sub></font>()
<b>by </b><i><a class="txt" href="#E1:88_1"><i><font color="Green" title="E71">A1</font></i></a>, <a class="ref" href="modelc_1.html#D41" target="_self" title="MODELC_1:def.41">Def41</a></i>
<br/>.= 
 <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">g2</font>,<font color="Maroon">F<sub>1</sub></font>()
<b>by </b><i><a class="txt" href="#E5:88_1"><i><font color="Green" title="E75">A5</font></i></a>, <a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</a></i>
<br/>.= 
<font color="Maroon" title="c2">g2</font>
<b>by </b><i><a class="txt" href="#E3:88_1"><i><font color="Green" title="E73">A3</font></i></a>, <a class="ref" href="modelc_1.html#D41" target="_self" title="MODELC_1:def.41">Def41</a></i>
;<br/>
<b>hence </b><a NAME="E7:88_1"/>
<font color="Maroon" title="c1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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