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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] means ex <font color="Olive">b<sub>1</sub></font> being  <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="partfun1.html#V1" target="_self">total</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#R1" target="_self">tolerates</a> <font color="Olive">b<sub>1</sub></font> );<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_1_1_1"><b>now </b></a><div class="add"><b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:105_1_1_1"/><i><font color="Green">E49</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K4" target="_self">PFuncs</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i><b>take </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>thus </b><a NAME="E3:105_1_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="partfun1.html#V1" target="_self">total</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#R1" target="_self">tolerates</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="partfun1.html#E2:105_1_1_1"><i><font color="Green">E49</font></i></a></i>;<br/><b>given </b><font color="Maroon">c<sub>7</sub></font> being   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><a NAME="E4:105_1_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E5:105_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> is <a href="partfun1.html#V1" target="_self">total</a>
 <b>and </b><br/><a NAME="E6:105_1_1_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#R1" target="_self">tolerates</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E7:105_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K4" target="_self">PFuncs</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="partfun1.html#T119" target="_self">Th119</a></i>;<br/><b>hence </b><a NAME="E8:105_1_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="partfun1.html#E2:105_1_1_1"><i><font color="Green">E49</font></i></a>, <a class="txt" href="partfun1.html#E4:105_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="partfun1.html#E5:105_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="partfun1.html#E6:105_1_1_1"><i><font color="Green">E52</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:105_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> iff ex <font color="Olive">b<sub>3</sub></font> being  <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> is <a href="partfun1.html#V1" target="_self">total</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#R1" target="_self">tolerates</a> <font color="Olive">b<sub>3</sub></font> ) )
 ;<br/>


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