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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">  ex <font color="Olive" title="b1">o</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <span class="p2">(<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></span>)</span> st <br/>for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">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> &amp; <font color="Olive" title="b3">g</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">o</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K38" title="MODELC_2:func.38">And_0</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font>,<font color="Maroon" title="c1">S</font></span><br/>

<span class="kw">set </span><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/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <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="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>) <span class="kw">-&gt; </span>   <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#K38" title="MODELC_2:func.38">And_0</a> $1,$2,<font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c3">o</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <span class="p2">(<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></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:135"/><span class="lab"><font color="Green" title="E109">A1</font></span>: 
for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <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> holds  <font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="binop_1.html#S4" title="BINOP_1:sch.4">BINOP_1:sch 4</a>();<br/></span>
<a NAME="E3:135"/>
for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">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> &amp; <font color="Olive" title="b2">g</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="Maroon" title="c3">o</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K38" title="MODELC_2:func.38">And_0</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font>,<font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:135"><span class="lab"><font color="Green" title="E109">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:135"/>
 ex <font color="Olive" title="b1">o</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <span class="p2">(<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></span>)</span> st <br/>for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">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> &amp; <font color="Olive" title="b3">g</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">o</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K38" title="MODELC_2:func.38">And_0</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</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"> verum</span><br/>


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