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<b>let </b><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">c1</font>, <font color="Maroon" title="c4">c2</font>, <font color="Maroon" title="c5">c3</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C</font>;<br/><b>let </b><font color="Maroon" title="c6">F</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c2">D</font>;<br/><b>let </b><font color="Maroon" title="c7">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">D</font>;<br/>













<b>assume </b><b>that </b><br/><a NAME="E1:4"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c6">F</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Maroon" title="c6">F</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> )
 <b>and </b><br/><a NAME="E2:4"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c3">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c2</font>
 ;<br/>

<b>assume </b><a NAME="E3:4"/>
( <font color="Maroon" title="c3">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c3</font> &amp; <font color="Maroon" title="c4">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c3</font> )
 ;<br/>

<a NAME="E4:4"/><b>then </b><i><font color="Green" title="E7">A3</font></i>: 
( not <font color="Maroon" title="c5">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">c1</font>,<font color="Maroon" title="c4">c2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">c1</font>,<font color="Maroon" title="c4">c2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c6">F</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><font color="Maroon" title="c3">c1</font>,<font color="Maroon" title="c4">c2</font>,<font color="Maroon" title="c5">c3</font></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>,<font color="Maroon" title="c7">f</font> = 
<font color="Maroon" title="c6">F</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <span class="p1">(<span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default"><font color="Maroon" title="c3">c1</font>,<font color="Maroon" title="c4">c2</font></span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p2"><a href="setwiseo.html#K2" title="SETWISEO:func.2">{.</a><span class="default"><font color="Maroon" title="c5">c3</font></span><a href="setwiseo.html#K2" title="SETWISEO:func.2">.}</a></span></span>)</span>,<font color="Maroon" title="c7">f</font>
<b>by </b><i><a class="ref" href="enumset1.html#T43" title="ENUMSET1:th.43">ENUMSET1:43</a></i>
<br/>.= 
<font color="Maroon" title="c6">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default"><font color="Maroon" title="c3">c1</font>,<font color="Maroon" title="c4">c2</font></span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<font color="Maroon" title="c7">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c3</font></span>)</span>
<b>by </b><i><a class="txt" href="setwop_2.html#E1:4"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="setwop_2.html#E4:4"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="setwop_2.html#T4" target="_self" title="SETWOP_2:th.4">Th4</a></i>
<br/>.= 
<font color="Maroon" title="c6">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">c1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c3</font></span>)</span>
<b>by </b><i><a class="txt" href="setwop_2.html#E1:4"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="setwop_2.html#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="setwop_2.html#T3" target="_self" title="SETWOP_2:th.3">Th3</a></i>
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