<?xml version="1.0"?>
<div class="add">

<span class="kw">set </span><font color="Maroon" title="c2">M</font> =  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">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#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">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#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">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#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> = <span class="p1">(<span class="default"><a href="modelc_2.html#K31" title="MODELC_2:func.31">Not_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K36" title="MODELC_2:func.36">And_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_2.html#K31" title="MODELC_2:func.31">Not_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> $1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_2.html#K31" title="MODELC_2:func.31">Not_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> $2</span>)</span>)</span>)</span>;<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#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:141_1_1"/><span class="lab"><font color="Green" title="E100">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#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">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" onmouseover="rs('binop_1/S4')" onmouseout="rh()">BINOP_1:sch 4</a>();<br/></span>
<a NAME="E3:141_1_1"/>
 for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> &amp; <font color="Olive" title="b2">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">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> <span class="p1">(<span class="default"><a href="modelc_2.html#K31" title="MODELC_2:func.31">Not_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K36" title="MODELC_2:func.36">And_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_2.html#K31" title="MODELC_2:func.31">Not_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_2.html#K31" title="MODELC_2:func.31">Not_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">g</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:141_1_1"><span class="lab"><font color="Green" title="E100">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:141_1_1"/>
 ex <font color="Olive">b<sub>1</sub></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#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">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#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b2">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> &amp; <font color="Olive" title="b3">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="modelc_2.html#K31" title="MODELC_2:func.31">Not_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K36" title="MODELC_2:func.36">And_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_2.html#K31" title="MODELC_2:func.31">Not_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">f</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_2.html#K31" title="MODELC_2:func.31">Not_</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">g</font></span>)</span>)</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
