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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font>,   <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font>,   <a href="hidden.html#M1">set</a> ] means <font color="Maroon">a<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K3">odf</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">a<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K7">compf</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a<sub>2</sub></font></span>)</span>;<br/>
<a NAME="E1:12_1_1"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>]
 
;<br/>
<a NAME="E2:12_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font> st <br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>]
 
<b>from </b><i><a class="ref" href="binop_1.html#S3">BINOP_1:sch 3</a>(<a class="txt" href="realset3.html#E1:12_1_1"><i><font color="Green">E9</font></i></a>);<br/></i>
<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="binop_1.html#NM2">BinOp</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:12_1_1"/><i><font color="Green">E10</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K3">odf</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K7">compf</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span>
 ;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>thus </b><a NAME="E5:12_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K3">odf</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K7">compf</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="realset3.html#E4:12_1_1"><i><font color="Green">E10</font></i></a></i>;<br/>


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