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<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">S</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>,  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">S</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>) <span class="kw">-&gt; </span>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <span class="p1">(<span class="default"><a href="modelc_1.html#K4" title="MODELC_1:func.4">Castboolean</a> <span class="p2">(<span class="default">$2 <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1</span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K4" title="MODELC_1:func.4">Castboolean</a> <span class="p2">(<span class="default">$3 <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1</span>)</span></span>)</span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">IT</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E2:110_1_1"/><span class="lab"><font color="Green" title="E83">A1</font></span>: 
<font color="Maroon" title="c4">IT</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K31" title="MODELC_1:func.31">ModelSP</a> <font color="Maroon" title="c1">S</font>
 <span class="kw">and </span><br/><a NAME="E3:110_1_1"/><span class="lab"><font color="Green" title="E84">A2</font></span>: 
 for <font color="Olive" title="b1">s</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">S</font> holds <br/>( <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">s</font>, <a href="modelc_1.html#K32" title="MODELC_1:func.32">Fid</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">S</font>), <a href="modelc_1.html#K32" title="MODELC_1:func.32">Fid</a> (<font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c1">S</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">Fid</a> (<font color="Maroon" title="c4">IT</font>,<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">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="modelc_1.html#S6" target="_self" title="MODELC_1:sch.6">MODELC_1:sch 6</a>();<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c4">IT</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">IT</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_1.html#K31" title="MODELC_1:func.31">ModelSP</a> <font color="Maroon" title="c1">S</font> &amp; (  for <font color="Olive" title="b1">s</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">S</font> holds <br/>( <span class="p1">(<span class="default"><a href="modelc_1.html#K4" title="MODELC_1:func.4">Castboolean</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">Fid</a> (<font color="Maroon" title="c2">f</font>,<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">s</font></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K4" title="MODELC_1:func.4">Castboolean</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">Fid</a> (<font color="Maroon" title="c3">g</font>,<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">s</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">Fid</a> (<font color="Maroon" title="c4">IT</font>,<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">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) ) )</span><br/>

<span class="kw">thus </span><a NAME="E4:110_1_1"/>
( <font color="Maroon" title="c4">IT</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_1.html#K31" title="MODELC_1:func.31">ModelSP</a> <font color="Maroon" title="c1">S</font> &amp; (  for <font color="Olive" title="b1">s</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">S</font> holds <br/>( <span class="p1">(<span class="default"><a href="modelc_1.html#K4" title="MODELC_1:func.4">Castboolean</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">Fid</a> (<font color="Maroon" title="c2">f</font>,<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">s</font></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K4" title="MODELC_1:func.4">Castboolean</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">Fid</a> (<font color="Maroon" title="c3">g</font>,<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">s</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">Fid</a> (<font color="Maroon" title="c4">IT</font>,<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">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:110_1_1"><span class="lab"><font color="Green" title="E83">A1</font></span></a>, <a class="txt" href="#E3:110_1_1"><span class="lab"><font color="Green" title="E84">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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