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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>  st <font color="Olive" title="b1">a</font> <a href="normform.html#K3" title="NORMFORM:func.3">\</a> <font color="Olive" title="b2">b</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b1">a</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <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><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#K3" title="NORMFORM:func.3">\</a> <font color="Maroon" title="c4">b</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Maroon" title="c5">c</font> implies <font color="Maroon" title="c3">a</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <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><br/>









<b>assume </b><a NAME="E1:14"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K3" title="NORMFORM:func.3">\</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">c</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="normform.html#K3" title="NORMFORM:func.3">\</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">c</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="normform.html#D1" target="_self" title="NORMFORM:def.1">NORMFORM:def 1</a> <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#R1" title="NORMFORM:pred.1">c=</a> <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><br/>

<a NAME="E2:14"/><b>then </b>
( <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#K2" title="FINSUB_1:func.2">\</a> <span class="p1">(<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="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">c</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  &amp; <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#K2" title="FINSUB_1:func.2">\</a> <span class="p1">(<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="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">c</font> <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>;<br/>
<a NAME="E3:14"/><b>then </b>
( <font color="Maroon" title="c3">a</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<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="p1">(<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> &amp; <font color="Maroon" title="c3">a</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<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="p1">(<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> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T44" title="XBOOLE_1:th.44">XBOOLE_1:44</a></i>;<br/>
<b>hence </b><a NAME="E4:14"/>
( <font color="Maroon" title="c3">a</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  &amp; <font color="Maroon" title="c3">a</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="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>; <i><font color="Red">:: according to </font></i><a class="ref" href="normform.html#D1" target="_self" title="NORMFORM:def.1">NORMFORM:def 1</a> <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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