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<b>let </b><font color="Maroon">S</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">R</font> be  <a href="partfun1.html#V1">total</a>  <a href="relset_1.html#M2">Relation</a> of <font color="Maroon">S</font>,<font color="Maroon">S</font>;<br/>



<b>set </b><font color="Maroon">M</font> =  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font>,   <a href="subset_1.html#M1">Element</a> of  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font> =  <a href="modelc_1.html#K45" target="_self">EUntill_0</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>,<font color="Maroon">R</font>;<br/>
<b>consider </b><font color="Maroon">o</font> being   <a href="binop_1.html#NM2">BinOp</a> of  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font><b> such that </b><br/><a NAME="E2:113"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">f</font>, <font color="Olive">g</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font> holds  <font color="Maroon">o</font> <a href="binop_1.html#K2">.</a> <font color="Olive">f</font>,<font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">f</font>,<font color="Olive">g</font>)
 <b>from </b><i><a class="ref" href="binop_1.html#S4">BINOP_1:sch 4</a>();<br/></i>
<a NAME="E3:113"/>
for <font color="Olive">f</font>, <font color="Olive">g</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font> &amp; <font color="Olive">g</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font> holds <br/><font color="Maroon">o</font> <a href="binop_1.html#K1">.</a> <font color="Olive">f</font>,<font color="Olive">g</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K45" target="_self">EUntill_0</a> <font color="Olive">f</font>,<font color="Olive">g</font>,<font color="Maroon">R</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E29"><i><font color="Green">Lemma92</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:113"/>
 ex <font color="Olive">o</font> being  <a href="binop_1.html#NM2">BinOp</a> of  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font> st <br/>for <font color="Olive">f</font>, <font color="Olive">g</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font> &amp; <font color="Olive">g</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font> holds <br/><font color="Olive">o</font> <a href="binop_1.html#K1">.</a> <font color="Olive">f</font>,<font color="Olive">g</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K45" target="_self">EUntill_0</a> <font color="Olive">f</font>,<font color="Olive">g</font>,<font color="Maroon">R</font>
 ;<br/>


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