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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finsub_1.html#V4" title="FINSUB_1:attr.4">preBoolean</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds  <font color="Olive" title="b1">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Olive" title="b3">c</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c5">c</font></span>)</span></span><br/>









<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>now </b></a><div class="add"><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c5">c</font></span>)</span></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c5">c</font></span>)</span></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c5">c</font></span>)</span></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c5">c</font></span>)</span></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c5">c</font></span>)</span></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c5">c</font></span>)</span></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:6"/>
<font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K2" title="NORMFORM:func.2">/\</a> <font color="Maroon" title="c5">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="domain_1.html#T12" title="DOMAIN_1:th.12">DOMAIN_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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