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<div class="add">

<b>let </b><font color="Maroon" title="c1">S</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">R</font> being <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">BASSIGN</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</span><br/> for <font color="Olive" title="b3">T1</font>, <font color="Olive" title="b4">T2</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>  st  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Olive" title="b3">T1</font>,<font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">BASSIGN</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Olive" title="b4">T2</font>,<font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">BASSIGN</font> holds <br/><font color="Olive" title="b3">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">T2</font></span><br/><b>let </b><font color="Maroon" title="c2">R</font> be  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">S</font>,<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">BASSIGN</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</span><br/> for <font color="Olive" title="b2">T1</font>, <font color="Olive" title="b3">T2</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>  st  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Olive" title="b2">T1</font>,<font color="Maroon" title="c2">R</font>,<font color="Olive" title="b1">BASSIGN</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Olive" title="b3">T2</font>,<font color="Maroon" title="c2">R</font>,<font color="Olive" title="b1">BASSIGN</font> holds <br/><font color="Olive" title="b2">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">T2</font></span><br/><b>let </b><font color="Maroon" title="c3">BASSIGN</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</span>; <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">T1</font>, <font color="Olive" title="b2">T2</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>  st  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Olive" title="b1">T1</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Olive" title="b2">T2</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font> holds <br/><font color="Olive" title="b1">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">T2</font></span><br/><b>let </b><font color="Maroon" title="c4">T1</font>, <font color="Maroon" title="c5">T2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <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"> (  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c4">T1</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c5">T2</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font> implies <font color="Maroon" title="c4">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">T2</font> )</span><br/>







<b>set </b><font color="Maroon" title="c6">h1</font> =  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c4">T1</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>;<br/>
<b>set </b><font color="Maroon" title="c7">h2</font> =  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c5">T2</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>;<br/>
<b>assume </b><a NAME="E1:151"/><i><font color="Green" title="E113">A1</font></i>: 
 <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c4">T1</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c5">T2</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="c4">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">T2</font></span><br/>

<a NAME="E2:151"/><i><font color="Green" title="E114">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" title="c4">T1</font> holds <br/><font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">T2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="151_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">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="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">T1</font> implies <font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">T2</font> )</span><br/>

<b>assume </b><a NAME="E1:151_1"/><i><font color="Green" title="E115">A3</font></i>: 
<font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">T1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">T2</font></span><br/>

<a NAME="E2:151_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="funct_3.html#K5" title="FUNCT_3:func.5">chi</a> <font color="Maroon" title="c4">T1</font>,<font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="funct_3.html#D3" title="FUNCT_3:def.3">FUNCT_3:def 3</a></i>;<br/>
<a NAME="E3:151_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c4">T1</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font></span>)</span>,<font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">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="modelc_1.html#E1:151_1"><i><font color="Green" title="E115">A3</font></i></a>, <a class="ref" href="modelc_1.html#D64" target="_self" title="MODELC_1:def.64">Def64</a></i>;<br/>
<a NAME="E4:151_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="funct_3.html#K5" title="FUNCT_3:func.5">chi</a> <font color="Maroon" title="c5">T2</font>,<font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:151"><i><font color="Green" title="E113">A1</font></i></a>, <a class="txt" href="modelc_1.html#E1:151_1"><i><font color="Green" title="E115">A3</font></i></a>, <a class="ref" href="modelc_1.html#D64" target="_self" title="MODELC_1:def.64">Def64</a></i>;<br/>
<b>hence </b><a NAME="E5:151_1"/>
<font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">T2</font>
 <b>by </b><i><a class="ref" href="funct_3.html#T42" title="FUNCT_3:th.42">FUNCT_3:42</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>
<a NAME="E3:151"/>
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" title="c5">T2</font> holds <br/><font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">T1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="151_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">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="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">T2</font> implies <font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">T1</font> )</span><br/>

<b>assume </b><a NAME="E1:151_2"/><i><font color="Green" title="E115">A4</font></i>: 
<font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">T2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">T1</font></span><br/>

<a NAME="E2:151_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="funct_3.html#K5" title="FUNCT_3:func.5">chi</a> <font color="Maroon" title="c5">T2</font>,<font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="funct_3.html#D3" title="FUNCT_3:def.3">FUNCT_3:def 3</a></i>;<br/>
<a NAME="E3:151_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c5">T2</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font></span>)</span>,<font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">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="modelc_1.html#E1:151_2"><i><font color="Green" title="E115">A4</font></i></a>, <a class="ref" href="modelc_1.html#D64" target="_self" title="MODELC_1:def.64">Def64</a></i>;<br/>
<a NAME="E4:151_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="funct_3.html#K5" title="FUNCT_3:func.5">chi</a> <font color="Maroon" title="c4">T1</font>,<font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:151"><i><font color="Green" title="E113">A1</font></i></a>, <a class="txt" href="modelc_1.html#E1:151_2"><i><font color="Green" title="E115">A4</font></i></a>, <a class="ref" href="modelc_1.html#D64" target="_self" title="MODELC_1:def.64">Def64</a></i>;<br/>
<b>hence </b><a NAME="E5:151_2"/>
<font color="Maroon" title="c8">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">T1</font>
 <b>by </b><i><a class="ref" href="funct_3.html#T42" title="FUNCT_3:th.42">FUNCT_3:42</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>
<b>hence </b><a NAME="E4:151"/>
<font color="Maroon" title="c4">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">T2</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E2:151"><i><font color="Green" title="E114">A2</font></i></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</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>
