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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finsub_1.html#V4">preBoolean</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>







<a NAME="E1:13"/><i><font color="Green">E13</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="domain_1.html#K2">`1</a> </span>)</span> <a href="finsub_1.html#K2">\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="domain_1.html#K2">`1</a> </span>)</span></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="domain_1.html#K2">`1</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="domain_1.html#K2">`1</a> </span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="domain_1.html#K2">`1</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="domain_1.html#K3">`2</a> </span>)</span> <a href="finsub_1.html#K2">\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="domain_1.html#K3">`2</a> </span>)</span></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="domain_1.html#K3">`2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="domain_1.html#K3">`2</a> </span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="domain_1.html#K3">`2</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>;<br/>
<a NAME="E2:13"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="normform.html#K3" target="_self">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="domain_1.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="domain_1.html#K2">`1</a> </span>)</span> <a href="finsub_1.html#K2">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="domain_1.html#K2">`1</a> </span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="normform.html#K3" target="_self">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="domain_1.html#K3">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="domain_1.html#K3">`2</a> </span>)</span> <a href="finsub_1.html#K2">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="domain_1.html#K3">`2</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E3:13"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="normform.html#K3" target="_self">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="domain_1.html#K2">`1</a> </span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="domain_1.html#K2">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="normform.html#K3" target="_self">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="domain_1.html#K3">`2</a> </span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="domain_1.html#K3">`2</a> </span>)</span></span>)</span></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="txt" href="normform.html#E1:13"><i><font color="Green">E13</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:13"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="normform.html#K3" target="_self">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>


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