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<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">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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>



<b>assume </b><b>that </b><br/><a NAME="E1:160"/><i><font color="Green" title="E131">C1</font></i>: 
<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>
 <b>and </b><br/><a NAME="E2:160"/><i><font color="Green" title="E132">C2</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E3:160"/><i><font color="Green" title="E133">C3</font></i>: 
 <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:()"><i><font color="Red">::  thesis: </font></i></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="E4:160"/>
 <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>
 
<b>by </b><i><a class="txt" href="modelc_2.html#E1:160"><i><font color="Green" title="E131">C1</font></i></a>, <a class="ref" href="modelc_1.html#D41" title="MODELC_1:def.41">MODELC_1:def 41</a></i>;<br/>
<b>hence </b><a NAME="E5:160"/>
<font color="Maroon" title="c2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:160"><i><font color="Green" title="E132">C2</font></i></a>, <a class="ref" href="modelc_1.html#D41" title="MODELC_1:def.41">MODELC_1:def 41</a>, <a class="txt" href="modelc_2.html#E3:160"><i><font color="Green" title="E133">C3</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/>


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