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<b>let </b><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>;<br/><b>let </b><font color="Maroon" title="c6">X</font>, <font color="Maroon" title="c7">Y</font>, <font color="Maroon" title="c8">Z</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:81"/><i><font color="Green" title="E66">A1</font></i>: 
( <font color="Maroon" title="c6">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  &amp; <font color="Maroon" title="c7">Y</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  &amp; <font color="Maroon" title="c8">Z</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  &amp; <font color="Maroon" title="c6">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c7">Y</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Z</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Z</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">Y</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Z</font> &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">Y</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Z</font> &amp; <font color="Maroon" title="c6">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">Y</font> )
 <b>and </b><br/><a NAME="E2:81"/><i><font color="Green" title="E67">A2</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">d</font> )
 ;<br/>

<a NAME="E3:81"/><i><font color="Green" title="E68">A3</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:81"><i><font color="Green" title="E66">A1</font></i></a>, <a class="ref" href="aff_4.html#T63" target="_self" title="AFF_4:th.63">Th63</a></i>;<br/>
<a NAME="E4:81"/><i><font color="Green" title="E69">A4</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">Z</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">Z</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">Y</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">Z</font> &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">Y</font> &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">Z</font> )
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:81"><i><font color="Green" title="E66">A1</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">A</font> = <font color="Maroon" title="c6">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Z</font>;<br/>
<b>set </b><font color="Maroon" title="c10">C</font> = <font color="Maroon" title="c7">Y</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Z</font>;<br/>
<a NAME="E5:81"/><i><font color="Green" title="E70">A5</font></i>: 
<font color="Maroon" title="c8">Z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">Y</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:81"><i><font color="Green" title="E66">A1</font></i></a>, <a class="txt" href="aff_4.html#E4:81"><i><font color="Green" title="E69">A4</font></i></a>, <a class="txt" href="aff_4.html#E79"><i><font color="Green" title="E64">Lm13</font></i></a></i>;<br/>
<a NAME="E6:81"/>
<font color="Maroon" title="c8">Z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">X</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:81"><i><font color="Green" title="E66">A1</font></i></a>, <a class="txt" href="aff_4.html#E4:81"><i><font color="Green" title="E69">A4</font></i></a>, <a class="txt" href="aff_4.html#E79"><i><font color="Green" title="E64">Lm13</font></i></a></i>;<br/>
<a NAME="E7:81"/><b>then </b>
( <font color="Maroon" title="c6">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Z</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c7">Y</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Z</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:81"><i><font color="Green" title="E66">A1</font></i></a>, <a class="txt" href="aff_4.html#E2:81"><i><font color="Green" title="E67">A2</font></i></a>, <a class="txt" href="aff_4.html#E4:81"><i><font color="Green" title="E69">A4</font></i></a>, <a class="txt" href="aff_4.html#E5:81"><i><font color="Green" title="E70">A5</font></i></a>, <a class="ref" href="aff_4.html#T24" target="_self" title="AFF_4:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E8:81"/>
<font color="Maroon" title="c6">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c7">Y</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Z</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:81"><i><font color="Green" title="E66">A1</font></i></a>, <a class="txt" href="aff_4.html#E2:81"><i><font color="Green" title="E67">A2</font></i></a>, <a class="txt" href="aff_4.html#E3:81"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>


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