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<b>let </b><font color="Maroon">S1</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font>, <font color="Maroon">S2</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:12_1_2"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font> holds  <font color="Maroon">S1</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K3">odf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K7">compf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font></span>)</span>
 <b>and </b><br/><a NAME="E2:12_1_2"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font> holds  <font color="Maroon">S2</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K3">odf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K7">compf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:12_1_2_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <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">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:12_1_2_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><b>thus </b><font color="Maroon">S1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> = 
<font color="Maroon">S1</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
<b>by </b><i><a class="ref" href="realset3.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K3">odf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K7">compf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, <a class="ref" href="realset3.html#T3" target="_self">Th3</a></i>
<br/>.= 
<font color="Maroon">S2</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
<b>by </b><i><a class="ref" href="realset3.html#T2" target="_self">Th2</a>, <a class="ref" href="realset3.html#T3" target="_self">Th3</a></i>
<br/>.= 
<font color="Maroon">S2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font>
<b>by </b><i><a class="ref" href="realset3.html#T3" target="_self">Th3</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:12_1_2"/>
<font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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