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<b>let </b><font color="Maroon" title="c4">Y1</font>, <font color="Maroon" title="c5">Y2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y1</font> &amp; <font color="Maroon" title="c3">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c4">Y1</font> &amp; <font color="Maroon" title="c4">Y1</font> is <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y2</font> &amp; <font color="Maroon" title="c3">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c5">Y2</font> &amp; <font color="Maroon" title="c5">Y2</font> is <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a> implies <font color="Maroon" title="c4">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Y2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:82_1_1"/><i><font color="Green" title="E68">A2</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y1</font> &amp; <font color="Maroon" title="c3">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c4">Y1</font> &amp; <font color="Maroon" title="c4">Y1</font> is <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a> )
 <b>and </b><br/><a NAME="E2:82_1_1"/><i><font color="Green" title="E69">A3</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y2</font> &amp; <font color="Maroon" title="c3">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c5">Y2</font> &amp; <font color="Maroon" title="c5">Y2</font> is <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Y2</font></span><br/>

<a NAME="E3:82_1_1"/>
<font color="Maroon" title="c4">Y1</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c5">Y2</font>
 
<b>by </b><i><a class="txt" href="#E1:82"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="#E1:82_1_1"><i><font color="Green" title="E68">A2</font></i></a>, <a class="txt" href="#E2:82_1_1"><i><font color="Green" title="E69">A3</font></i></a>, <a class="ref" href="aff_4.html#T61" target="_self" title="AFF_4:th.61">Th61</a></i>;<br/>
<b>hence </b><a NAME="E4:82_1_1"/>
<font color="Maroon" title="c4">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Y2</font>
 <b>by </b><i><a class="txt" href="#E1:82_1_1"><i><font color="Green" title="E68">A2</font></i></a>, <a class="txt" href="#E2:82_1_1"><i><font color="Green" title="E69">A3</font></i></a>, <a class="txt" href="aff_4.html#E79"><i><font color="Green" title="E64">Lm13</font></i></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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