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<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  =  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">IFEQ</a> $1,<a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a> ,<a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ;<br/>
<b>consider </b><font color="Maroon" title="c2">V</font> being    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E2:78_1_2"/><i><font color="Green" title="E41">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> holds <br/><font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">x</font>)
 <b>from </b><i><a class="ref" href="pboole.html#S4" title="PBOOLE:sch.4">PBOOLE:sch 4</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c2">V</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  )</span><br/>

<a NAME="E3:78_1_2"/><i><font color="Green" title="E42">A2</font></i>: 
(  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">IFEQ</a> <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a> ,<a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a> ,<a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">IFEQ</a> <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a> ,<a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a> ,<a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">IFEQ</a> <a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a> ,<a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a> ,<a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  )
 
<b>by </b><i><a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>;<br/>
<a NAME="E4:78_1_2"/>
(  <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp;  <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp;  <a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> )
 
<b>by </b><i><a class="txt" href="#E1:78"><i><font color="Green" title="E40">A0</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:78_1_2"/>
( <font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  )
 <b>by </b><i><a class="txt" href="#E2:78_1_2"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="#E3:78_1_2"><i><font color="Green" title="E42">A2</font></i></a></i>; <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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