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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be  non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">d</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">b9</font>, <font color="Olive" title="b5">d9</font>, <font color="Olive" title="b6">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>  st not <font color="Olive" title="b6">q</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">d</font>,<font color="Olive" title="b1">x</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b6">q</font>,<font color="Olive" title="b4">b9</font>,<font color="Olive" title="b3">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b6">q</font>,<font color="Olive" title="b5">d9</font>,<font color="Olive" title="b2">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  holds <br/> ex <font color="Olive" title="b7">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b5">d9</font>,<font color="Olive" title="b7">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b6">q</font>,<font color="Olive" title="b1">x</font>,<font color="Olive" title="b7">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">d</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">b9</font>, <font color="Maroon" title="c6">d9</font>, <font color="Maroon" title="c7">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c2">x</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c4">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c6">d9</font>,<font color="Maroon" title="c3">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  implies  ex <font color="Olive" title="b1">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  ) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:97"/><span class="lab"><font color="Green" title="E84">A1</font></span>: 
not <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E2:97"/><span class="lab"><font color="Green" title="E85">A2</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c2">x</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E3:97"/><span class="lab"><font color="Green" title="E86">A3</font></span>: 
<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c4">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E4:97"/><span class="lab"><font color="Green" title="E87">A4</font></span>: 
<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c6">d9</font>,<font color="Maroon" title="c3">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/>

<a NAME="E5:97"/><span class="lab"><font color="Green" title="E88">A5</font></span>: 
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c4">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E86">A3</font></span></a>, <a class="ref" href="anproj_2.html#T25" target="_self" title="ANPROJ_2:th.25">Th25</a></span>;<br/>
<a NAME="E6:97"/><span class="lab"><font color="Green" title="E89">A6</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E84">A1</font></span></a>, <a class="ref" href="anproj_2.html#D7" target="_self" title="ANPROJ_2:def.7">Def7</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E90">A7</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:97_1"/><span class="lab"><font color="Green" title="E91">A8</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E86">A3</font></span></a>, <a class="ref" href="anproj_2.html#T25" target="_self" title="ANPROJ_2:th.25">Th25</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c8">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:97_1"/><span class="lab"><font color="Green" title="E92">A9</font></span>: 
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font>,<font color="Maroon" title="c8">z</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E4:97_1"/><span class="lab"><font color="Green" title="E93">A10</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c8">z</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:97"><span class="lab"><font color="Green" title="E87">A4</font></span></a>, <a class="txt" href="#E5:97"><span class="lab"><font color="Green" title="E88">A5</font></span></a>, <a class="ref" href="anproj_2.html#D9" target="_self" title="ANPROJ_2:def.9">Def9</a></span>;<br/><a NAME="E5:97_1"/><span class="lab"><font color="Green" title="E94">A11</font></span>: 
<font color="Maroon" title="c8">z</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c5">b9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_2.html#D7" target="_self" title="ANPROJ_2:def.7">Def7</a></span>;<br/><a NAME="E6:97_1"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c4">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_2.html#D7" target="_self" title="ANPROJ_2:def.7">Def7</a></span>;<br/><a NAME="E7:97_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">z</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">x</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:97"><span class="lab"><font color="Green" title="E85">A2</font></span></a>, <a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E89">A6</font></span></a>, <a class="txt" href="#E4:97_1"><span class="lab"><font color="Green" title="E93">A10</font></span></a>, <a class="ref" href="anproj_2.html#D8" target="_self" title="ANPROJ_2:def.8">Def8</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">o</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E9:97_1"/><span class="lab"><font color="Green" title="E95">A12</font></span>: 
<font color="Maroon" title="c8">z</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c9">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E10:97_1"/><span class="lab"><font color="Green" title="E96">A13</font></span>: 
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c9">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1"><span class="lab"><font color="Green" title="E91">A8</font></span></a>, <a class="ref" href="anproj_2.html#D9" target="_self" title="ANPROJ_2:def.9">Def9</a></span>;<br/><a NAME="E11:97_1"/><span class="lab"><font color="Green" title="E97">A14</font></span>: 
<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c9">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:97_1"><span class="lab"><font color="Green" title="E96">A13</font></span></a>, <a class="ref" href="anproj_2.html#T25" target="_self" title="ANPROJ_2:th.25">Th25</a></span>;<br/><span class="kw">assume </span><a NAME="E12:97_1"/><span class="lab"><font color="Green" title="E98">A15</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/><a NAME="E13:97_1"/><span class="lab"><font color="Green" title="E99">A16</font></span>: 
<font color="Maroon" title="c8">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:97_1_1"/>
not <font color="Maroon" title="c8">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:97_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E100">A17</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c3">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:97_1"><span class="lab"><font color="Green" title="E93">A10</font></span></a>, <a class="ref" href="anproj_2.html#T25" target="_self" title="ANPROJ_2:th.25">Th25</a></span>;<br/>
<a NAME="E3:97_1_1"/>
( <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c4">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E86">A3</font></span></a>, <a class="ref" href="anproj_2.html#D7" target="_self" title="ANPROJ_2:def.7">Def7</a>, <a class="ref" href="anproj_2.html#T25" target="_self" title="ANPROJ_2:th.25">Th25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:97_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E84">A1</font></span></a>, <a class="txt" href="#E12:97_1"><span class="lab"><font color="Green" title="E98">A15</font></span></a>, <a class="txt" href="#E2:97_1_1"><span class="lab"><font color="Green" title="E100">A17</font></span></a>, <a class="ref" href="anproj_2.html#D8" target="_self" title="ANPROJ_2:def.8">Def8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E14:97_1"/>
<font color="Maroon" title="c8">z</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97_1"><span class="lab"><font color="Green" title="E92">A9</font></span></a>, <a class="ref" href="anproj_2.html#T25" target="_self" title="ANPROJ_2:th.25">Th25</a></span>;<br/><a NAME="E15:97_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font>,<font color="Maroon" title="c9">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:97_1"><span class="lab"><font color="Green" title="E95">A12</font></span></a>, <a class="txt" href="#E13:97_1"><span class="lab"><font color="Green" title="E99">A16</font></span></a>, <a class="txt" href="#E5:97_1"><span class="lab"><font color="Green" title="E94">A11</font></span></a>, <a class="ref" href="anproj_2.html#D8" target="_self" title="ANPROJ_2:def.8">Def8</a></span>;<br/><span class="kw">hence </span><a NAME="E16:97_1"/>
 ex <font color="Olive" title="b1">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:97_1"><span class="lab"><font color="Green" title="E97">A14</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:97_2"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/><a NAME="E2:97_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A18</font></span>: 
<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c2">x</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:97"><span class="lab"><font color="Green" title="E85">A2</font></span></a>, <a class="ref" href="anproj_2.html#T25" target="_self" title="ANPROJ_2:th.25">Th25</a></span>;<br/><a NAME="E3:97_2"/>
<font color="Maroon" title="c6">d9</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c7">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:97"><span class="lab"><font color="Green" title="E87">A4</font></span></a>, <a class="ref" href="anproj_2.html#T25" target="_self" title="ANPROJ_2:th.25">Th25</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">o</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E5:97_2"/><span class="lab"><font color="Green" title="E92">A19</font></span>: 
<font color="Maroon" title="c6">d9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c8">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E6:97_2"/><span class="lab"><font color="Green" title="E93">A20</font></span>: 
<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c8">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:97_2"><span class="lab"><font color="Green" title="E91">A18</font></span></a>, <a class="ref" href="anproj_2.html#D9" target="_self" title="ANPROJ_2:def.9">Def9</a></span>;<br/><a NAME="E7:97_2"/>
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font>,<font color="Maroon" title="c8">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:97_2"><span class="lab"><font color="Green" title="E92">A19</font></span></a>, <a class="ref" href="anproj_2.html#T25" target="_self" title="ANPROJ_2:th.25">Th25</a></span>;<br/><span class="kw">hence </span><a NAME="E8:97_2"/>
 ex <font color="Olive" title="b1">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97_2"><span class="lab"><font color="Green" title="E93">A20</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E9:97"/>
 ex <font color="Olive" title="b1">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">d9</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:97"><span class="lab"><font color="Green" title="E90">A7</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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