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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">o1</font>, <font color="Olive" title="b2">o2</font> being  <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of  <a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>  st ( for <font color="Olive" title="b3">f</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">f</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> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Not_0</a> <font color="Olive" title="b3">f</font>,<font color="Maroon" title="c1">S</font> ) &amp; ( for <font color="Olive" title="b3">f</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">f</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> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b2">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Not_0</a> <font color="Olive" title="b3">f</font>,<font color="Maroon" title="c1">S</font> ) holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">o2</font></span><br/>

<b>set </b><font color="Maroon" title="c2">M</font> =  <a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> =  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Not_0</a> $1,<font color="Maroon" title="c1">S</font>;<br/>
<a NAME="E1:127"/>
for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being  <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of  <a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>  st ( for <font color="Olive" title="b3">f</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">f</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> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b3">f</font>) ) &amp; ( for <font color="Olive" title="b3">f</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">f</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> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b2">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b3">f</font>) ) holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">o2</font>
 
<b>from </b><i><a class="ref" href="modelc_1.html#S5" title="MODELC_1:sch.5">MODELC_1:sch 5</a>();<br/></i>
<b>hence </b><a NAME="E2:127"/>
for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being  <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of  <a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>  st ( for <font color="Olive" title="b3">f</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">f</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> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Not_0</a> <font color="Olive" title="b3">f</font>,<font color="Maroon" title="c1">S</font> ) &amp; ( for <font color="Olive" title="b3">f</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">f</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> <span class="p1">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b2">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Not_0</a> <font color="Olive" title="b3">f</font>,<font color="Maroon" title="c1">S</font> ) holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">o2</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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