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<b>set </b><font color="Maroon" title="c3">M</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">D</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="closure2.html#M1" title="CLOSURE2:mode.1">Element</a> of  <a href="closure2.html#K6" title="CLOSURE2:func.6">Bool</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">D</font>) <b>-&gt; </b>   <a href="closure2.html#M1" title="CLOSURE2:mode.1">Element</a> of  <a href="closure2.html#K6" title="CLOSURE2:func.6">Bool</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">D</font> =  <a href="closure2.html#K11" title="CLOSURE2:func.11">Cl</a> $1;<br/>
<b>consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="closure2.html#K6" title="CLOSURE2:func.6">Bool</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">D</font>, <a href="closure2.html#K6" title="CLOSURE2:func.6">Bool</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">D</font><b> such that </b><br/><a NAME="E2:99_1_1"/><i><font color="Green" title="E40">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="closure2.html#M1" title="CLOSURE2:mode.1">Element</a> of  <a href="closure2.html#K6" title="CLOSURE2:func.6">Bool</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">D</font> holds  <font color="Maroon" title="c4">f</font> <a href="closure2.html#K7" title="CLOSURE2:func.7">.</a> <font color="Olive" title="b1">x</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4" title="FUNCT_2:sch.4">FUNCT_2:sch 4</a>();<br/></i>
<b>reconsider </b><font color="Maroon" title="c5">f</font> = <font color="Maroon" title="c4">f</font> as   <a href="closure2.html#NM3" title="CLOSURE2:NM.3">SetOp</a> of the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">D</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c6">f</font> = <font color="Maroon" title="c5">f</font> as   <a href="closure2.html#NM5" title="CLOSURE2:NM.5">ClosureOperator</a> of the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">D</font> <b>by </b><i><a class="txt" href="closure2.html#E2:99_1_1"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="closure2.html#T42" target="_self" title="CLOSURE2:th.42">Th42</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="closure2.html#M1" title="CLOSURE2:mode.1">Element</a> of  <a href="closure2.html#K6" title="CLOSURE2:func.6">Bool</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">D</font> holds  <font color="Maroon" title="c6">f</font> <a href="closure2.html#K7" title="CLOSURE2:func.7">.</a> <font color="Olive" title="b1">x</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="closure2.html#K11" title="CLOSURE2:func.11">Cl</a> <font color="Olive" title="b1">x</font></span><br/>

<b>thus </b><a NAME="E5:99_1_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="closure2.html#M1" title="CLOSURE2:mode.1">Element</a> of  <a href="closure2.html#K6" title="CLOSURE2:func.6">Bool</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">D</font> holds  <font color="Maroon" title="c6">f</font> <a href="closure2.html#K7" title="CLOSURE2:func.7">.</a> <font color="Olive" title="b1">x</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="closure2.html#K11" title="CLOSURE2:func.11">Cl</a> <font color="Olive" title="b1">x</font>
 <b>by </b><i><a class="txt" href="closure2.html#E2:99_1_1"><i><font color="Green" title="E40">A1</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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