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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="closure2.html#NM5">ClosureOperator</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:99_1_2"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> holds <font color="Maroon">c<sub>3</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R6">=</a>  <a href="closure2.html#K11" target="_self">Cl</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:99_1_2"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> holds <font color="Maroon">c<sub>4</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R6">=</a>  <a href="closure2.html#K11" target="_self">Cl</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_2_1"><b>now </b></a><div class="add"><b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>thus </b><a NAME="E1:99_1_2_1"/>
 <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>thus </b><a NAME="E2:99_1_2_1"/>
 <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E3:99_1_2_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="closure2.html#K11" target="_self">Cl</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="closure2.html#E1:99_1_2"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="closure2.html#E2:99_1_2"><i><font color="Green">E41</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:99_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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