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<span class="kw">let </span><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><br/>  for <font color="Olive" title="b2">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Olive" title="b2">X</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a>  holds <br/> ex <font color="Olive" title="b3">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">Y</font> &amp; <font color="Olive" title="b2">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Olive" title="b3">Y</font> &amp; <font color="Olive" title="b3">Y</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Olive" title="b1">X</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a>  holds <br/> ex <font color="Olive" title="b2">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">Y</font> &amp; <font color="Olive" title="b1">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Olive" title="b2">Y</font> &amp; <font color="Olive" title="b2">Y</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">X</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">X</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a>  implies  ex <font color="Olive" title="b1">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Maroon" title="c3">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b1">Y</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:81"/><span class="lab"><font color="Green" title="E67">A1</font></span>: 
<font color="Maroon" title="c3">X</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Maroon" title="c3">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b1">Y</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a>  )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</font>, <font color="Maroon" title="c6">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><span class="kw"> such that </span><br/><a NAME="E3:81"/><span class="lab"><font color="Green" title="E68">A2</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <span class="kw">and </span><br/><a NAME="E4:81"/><span class="lab"><font color="Green" title="E69">A3</font></span>: 
<font color="Maroon" title="c5">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <span class="kw">and </span><br/><a NAME="E5:81"/><span class="lab"><font color="Green" title="E70">A4</font></span>: 
<font color="Maroon" title="c6">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <span class="kw">and </span><br/><a NAME="E6:81"/><span class="lab"><font color="Green" title="E71">A5</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">r</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_4.html#T34" target="_self" title="AFF_4:th.34">Th34</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">M</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c8">N</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>);<br/>
<a NAME="E7:81"/><span class="lab"><font color="Green" title="E72">A6</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:81"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<a NAME="E8:81"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A7</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="txt" href="#E3:81"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E5:81"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">M9</font> = <font color="Maroon" title="c2">a</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">N9</font> = <font color="Maroon" title="c2">a</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>)</span>)</span>;<br/>
<a NAME="E9:81"/><span class="lab"><font color="Green" title="E74">A8</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:81"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<a NAME="E10:81"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A9</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>) is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></span>;<br/>
<a NAME="E11:81"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A10</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_4.html#T27" target="_self" title="AFF_4:th.27">Th27</a></span>;<br/>
<a NAME="E12:81"/><span class="lab"><font color="Green" title="E77">A11</font></span>: 
( <font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>) &amp; <font color="Maroon" title="c6">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E13:81"/><span class="lab"><font color="Green" title="E78">A12</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E14:81"/><span class="lab"><font color="Green" title="E79">A13</font></span>: 
<font color="Maroon" title="c5">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E15:81"/><span class="lab"><font color="Green" title="E80">A14</font></span>: 
 not  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:81_1"/>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:81"><span class="lab"><font color="Green" title="E78">A12</font></span></a>, <a class="txt" href="#E12:81"><span class="lab"><font color="Green" title="E77">A11</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:81_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:81"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E13:81"><span class="lab"><font color="Green" title="E78">A12</font></span></a>, <a class="txt" href="#E14:81"><span class="lab"><font color="Green" title="E79">A13</font></span></a>, <a class="txt" href="#E10:81"><span class="lab"><font color="Green" title="E75">A9</font></span></a>, <a class="ref" href="aff_1.html#T21" title="AFF_1:th.21">AFF_1:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E16:81"/><span class="lab"><font color="Green" title="E81">A15</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>) is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:81"><span class="lab"><font color="Green" title="E72">A6</font></span></a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></span>;<br/>
<a NAME="E17:81"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A16</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c2">a</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_4.html#D3" target="_self" title="AFF_4:def.3">Def3</a></span>;<br/>
<a NAME="E18:81"/><span class="lab"><font color="Green" title="E83">A17</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c2">a</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:81"><span class="lab"><font color="Green" title="E75">A9</font></span></a>, <a class="ref" href="aff_4.html#D3" target="_self" title="AFF_4:def.3">Def3</a></span>;<br/>
<a NAME="E19:81"/><span class="lab"><font color="Green" title="E84">A18</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:81"><span class="lab"><font color="Green" title="E75">A9</font></span></a>, <a class="ref" href="aff_4.html#D3" target="_self" title="AFF_4:def.3">Def3</a></span>;<br/>
<a NAME="E20:81"/>
( <font color="Maroon" title="c2">a</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>)</span>)</span> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>)</span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:81"><span class="lab"><font color="Green" title="E81">A15</font></span></a>, <a class="ref" href="aff_4.html#D3" target="_self" title="AFF_4:def.3">Def3</a>, <a class="ref" href="aff_4.html#T27" target="_self" title="AFF_4:th.27">Th27</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font><span class="kw"> such that </span><br/><a NAME="E22:81"/><span class="lab"><font color="Green" title="E85">A19</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">Y</font>
 <span class="kw">and </span><br/><a NAME="E23:81"/><span class="lab"><font color="Green" title="E86">A20</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="aff_4.html#K2" title="AFF_4:func.2">*</a> <span class="p1">(<span class="default"><a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">r</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">Y</font>
 <span class="kw">and </span><br/><a NAME="E24:81"/><span class="lab"><font color="Green" title="E87">A21</font></span>: 
<font color="Maroon" title="c11">Y</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:81"><span class="lab"><font color="Green" title="E76">A10</font></span></a>, <a class="txt" href="#E19:81"><span class="lab"><font color="Green" title="E84">A18</font></span></a>, <a class="ref" href="aff_4.html#T38" target="_self" title="AFF_4:th.38">Th38</a></span>;<br/>
<a NAME="E25:81"/>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="txt" href="#E3:81"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E4:81"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E9:81"><span class="lab"><font color="Green" title="E74">A8</font></span></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></span>;<br/>
<a NAME="E26:81"/><span class="kw">then </span>
<font color="Maroon" title="c3">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Maroon" title="c11">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="txt" href="#E18:81"><span class="lab"><font color="Green" title="E83">A17</font></span></a>, <a class="txt" href="#E17:81"><span class="lab"><font color="Green" title="E82">A16</font></span></a>, <a class="txt" href="#E22:81"><span class="lab"><font color="Green" title="E85">A19</font></span></a>, <a class="txt" href="#E23:81"><span class="lab"><font color="Green" title="E86">A20</font></span></a>, <a class="txt" href="#E24:81"><span class="lab"><font color="Green" title="E87">A21</font></span></a>, <a class="txt" href="#E8:81"><span class="lab"><font color="Green" title="E73">A7</font></span></a>, <a class="txt" href="#E15:81"><span class="lab"><font color="Green" title="E80">A14</font></span></a>, <a class="ref" href="aff_4.html#T55" target="_self" title="AFF_4:th.55">Th55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:81"/>
 ex <font color="Olive" title="b1">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Maroon" title="c3">X</font> <a href="aff_4.html#R1" title="AFF_4:pred.1">'||'</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b1">Y</font> is  <a href="aff_4.html#V1" title="AFF_4:attr.1">being_plane</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:81"><span class="lab"><font color="Green" title="E84">A18</font></span></a>, <a class="txt" href="#E22:81"><span class="lab"><font color="Green" title="E85">A19</font></span></a>, <a class="txt" href="#E24:81"><span class="lab"><font color="Green" title="E87">A21</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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