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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">f1</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" title="c1">S</font> &amp; <font color="Olive" title="b2">f2</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" title="c1">S</font> &amp;  <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Olive" title="b1">f1</font>,<font color="Maroon" title="c1">S</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Olive" title="b2">f2</font>,<font color="Maroon" title="c1">S</font> holds <br/><font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f1</font>, <font color="Maroon" title="c3">f2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">f1</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" title="c1">S</font> &amp; <font color="Maroon" title="c3">f2</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" title="c1">S</font> &amp;  <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">S</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c1">S</font> implies <font color="Maroon" title="c2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:159"/><span class="lab"><font color="Green" title="E131">A1</font></span>: 
<font color="Maroon" title="c2">f1</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" title="c1">S</font>
 <span class="kw">and </span><br/><a NAME="E2:159"/><span class="lab"><font color="Green" title="E132">A2</font></span>: 
<font color="Maroon" title="c3">f2</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" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not  <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">S</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c1">S</font> or <font color="Maroon" title="c2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:159"/><span class="lab"><font color="Green" title="E133">A3</font></span>: 
 <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">S</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font></span><br/>

<a NAME="E4:159"/>
 <a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:159"><span class="lab"><font color="Green" title="E131">A1</font></span></a>, <a class="ref" href="modelc_1.html#D41" title="MODELC_1:def.41">MODELC_1:def 41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:159"/>
<font color="Maroon" title="c2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:159"><span class="lab"><font color="Green" title="E132">A2</font></span></a>, <a class="txt" href="#E3:159"><span class="lab"><font color="Green" title="E133">A3</font></span></a>, <a class="ref" href="modelc_1.html#D41" title="MODELC_1:def.41">MODELC_1:def 41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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