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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">D</font>, <font color="Maroon">f2</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">g1</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">S</font>, <font color="Maroon">g2</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><a NAME="E1:5"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="realset1.html#K1">||</a> <font color="Maroon">S</font> &amp; <font color="Maroon">g2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="realset1.html#K1">||</a> <font color="Maroon">S</font> )
 ;<br/>

<b>assume </b><a NAME="E2:5"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> holds  <font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Olive">a</font>,<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Olive">a</font>,<font color="Olive">b</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">a</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice2.html#D1">LATTICE2:def 1</a><br/>

<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font>, <font color="Maroon">b</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice2.html#D1">LATTICE2:def 1</a><br/>

<a NAME="E3:5"/><i><font color="Green">E16</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">S</font></span><a href="mcart_1.html#K12">:]</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">S</font></span><a href="mcart_1.html#K12">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>thus </b><font color="Maroon">g1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> = 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>

<br/>.= 
<font color="Maroon">a</font>
<b>by </b><i/>
;<br/>


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