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<span class="kw">let </span><font color="Maroon" title="c1">CPS</font> be   <a href="anproj_2.html#NM1" title="ANPROJ_2:NM.1">CollProjectiveSpace</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">o</font>, <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</font>, <font color="Olive" title="b4">p3</font>, <font color="Olive" title="b5">q1</font>, <font color="Olive" title="b6">q2</font>, <font color="Olive" title="b7">q3</font>, <font color="Olive" title="b8">r1</font>, <font color="Olive" title="b9">r2</font>, <font color="Olive" title="b10">r3</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">CPS</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">p2</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">p3</font> &amp; <font color="Olive" title="b3">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">p3</font> &amp; <font color="Olive" title="b2">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">p2</font> &amp; <font color="Olive" title="b2">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">p3</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">q2</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">q3</font> &amp; <font color="Olive" title="b6">q2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">q3</font> &amp; <font color="Olive" title="b5">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">q2</font> &amp; <font color="Olive" title="b5">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">q3</font> &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b5">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b4">p3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b6">q2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b7">q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b6">q2</font>,<font color="Olive" title="b10">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b5">q1</font>,<font color="Olive" title="b3">p2</font>,<font color="Olive" title="b10">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b7">q3</font>,<font color="Olive" title="b9">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">p3</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b9">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">p2</font>,<font color="Olive" title="b7">q3</font>,<font color="Olive" title="b8">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">p3</font>,<font color="Olive" title="b6">q2</font>,<font color="Olive" title="b8">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  holds <br/><font color="Olive" title="b8">r1</font>,<font color="Olive" title="b9">r2</font>,<font color="Olive" title="b10">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  ) implies for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</font>, <font color="Olive" title="b5">b1</font>, <font color="Olive" title="b6">b2</font>, <font color="Olive" title="b7">b3</font>, <font color="Olive" title="b8">c1</font>, <font color="Olive" title="b9">c2</font>, <font color="Olive" title="b10">c3</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span><br/> for <font color="Olive" title="b11">A1</font>, <font color="Olive" title="b12">A2</font>, <font color="Olive" title="b13">A3</font>, <font color="Olive" title="b14">B1</font>, <font color="Olive" title="b15">B2</font>, <font color="Olive" title="b16">B3</font>, <font color="Olive" title="b17">C1</font>, <font color="Olive" title="b18">C2</font>, <font color="Olive" title="b19">C3</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span>  st <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b4">a3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">b1</font>,<font color="Olive" title="b6">b2</font>,<font color="Olive" title="b7">b3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  &amp; <font color="Olive" title="b13">A3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b16">B3</font> &amp; <font color="Olive" title="b1">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b13">A3</font> &amp; <font color="Olive" title="b1">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b16">B3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b3">a2</font>,<font color="Olive" title="b7">b3</font>,<font color="Olive" title="b8">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b11">A1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b4">a3</font>,<font color="Olive" title="b5">b1</font>,<font color="Olive" title="b9">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b14">B1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">a1</font>,<font color="Olive" title="b6">b2</font>,<font color="Olive" title="b10">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b17">C1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">a1</font>,<font color="Olive" title="b7">b3</font>,<font color="Olive" title="b9">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b12">A2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b4">a3</font>,<font color="Olive" title="b6">b2</font>,<font color="Olive" title="b8">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b15">B2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b3">a2</font>,<font color="Olive" title="b5">b1</font>,<font color="Olive" title="b10">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b18">C2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b5">b1</font>,<font color="Olive" title="b6">b2</font>,<font color="Olive" title="b7">b3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b13">A3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b4">a3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b16">B3</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b8">c1</font>,<font color="Olive" title="b9">c2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b19">C3</font> holds <br/><font color="Olive" title="b10">c3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b19">C3</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:27"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</font>, <font color="Olive" title="b4">p3</font>, <font color="Olive" title="b5">q1</font>, <font color="Olive" title="b6">q2</font>, <font color="Olive" title="b7">q3</font>, <font color="Olive" title="b8">r1</font>, <font color="Olive" title="b9">r2</font>, <font color="Olive" title="b10">r3</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">CPS</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">p2</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">p3</font> &amp; <font color="Olive" title="b3">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">p3</font> &amp; <font color="Olive" title="b2">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">p2</font> &amp; <font color="Olive" title="b2">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">p3</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">q2</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">q3</font> &amp; <font color="Olive" title="b6">q2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">q3</font> &amp; <font color="Olive" title="b5">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">q2</font> &amp; <font color="Olive" title="b5">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">q3</font> &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b5">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b4">p3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b6">q2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b7">q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b6">q2</font>,<font color="Olive" title="b10">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b5">q1</font>,<font color="Olive" title="b3">p2</font>,<font color="Olive" title="b10">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b7">q3</font>,<font color="Olive" title="b9">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">p3</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b9">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">p2</font>,<font color="Olive" title="b7">q3</font>,<font color="Olive" title="b8">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">p3</font>,<font color="Olive" title="b6">q2</font>,<font color="Olive" title="b8">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  holds <br/><font color="Olive" title="b8">r1</font>,<font color="Olive" title="b9">r2</font>,<font color="Olive" title="b10">r3</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"> for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</font>, <font color="Olive" title="b5">b1</font>, <font color="Olive" title="b6">b2</font>, <font color="Olive" title="b7">b3</font>, <font color="Olive" title="b8">c1</font>, <font color="Olive" title="b9">c2</font>, <font color="Olive" title="b10">c3</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span><br/> for <font color="Olive" title="b11">A1</font>, <font color="Olive" title="b12">A2</font>, <font color="Olive" title="b13">A3</font>, <font color="Olive" title="b14">B1</font>, <font color="Olive" title="b15">B2</font>, <font color="Olive" title="b16">B3</font>, <font color="Olive" title="b17">C1</font>, <font color="Olive" title="b18">C2</font>, <font color="Olive" title="b19">C3</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span>  st <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b4">a3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">b1</font>,<font color="Olive" title="b6">b2</font>,<font color="Olive" title="b7">b3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  &amp; <font color="Olive" title="b13">A3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b16">B3</font> &amp; <font color="Olive" title="b1">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b13">A3</font> &amp; <font color="Olive" title="b1">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b16">B3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b3">a2</font>,<font color="Olive" title="b7">b3</font>,<font color="Olive" title="b8">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b11">A1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b4">a3</font>,<font color="Olive" title="b5">b1</font>,<font color="Olive" title="b9">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b14">B1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">a1</font>,<font color="Olive" title="b6">b2</font>,<font color="Olive" title="b10">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b17">C1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">a1</font>,<font color="Olive" title="b7">b3</font>,<font color="Olive" title="b9">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b12">A2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b4">a3</font>,<font color="Olive" title="b6">b2</font>,<font color="Olive" title="b8">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b15">B2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b3">a2</font>,<font color="Olive" title="b5">b1</font>,<font color="Olive" title="b10">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b18">C2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b5">b1</font>,<font color="Olive" title="b6">b2</font>,<font color="Olive" title="b7">b3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b13">A3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b4">a3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b16">B3</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b8">c1</font>,<font color="Olive" title="b9">c2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b19">C3</font> holds <br/><font color="Olive" title="b10">c3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b19">C3</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c9">c1</font>, <font color="Maroon" title="c10">c2</font>, <font color="Maroon" title="c11">c3</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span>; <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">A1</font>, <font color="Olive" title="b2">A2</font>, <font color="Olive" title="b3">A3</font>, <font color="Olive" title="b4">B1</font>, <font color="Olive" title="b5">B2</font>, <font color="Olive" title="b6">B3</font>, <font color="Olive" title="b7">C1</font>, <font color="Olive" title="b8">C2</font>, <font color="Olive" title="b9">C3</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span>  st <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  &amp; <font color="Olive" title="b3">A3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">B3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">A3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b6">B3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b1">A1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c10">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b4">B1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c11">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b7">C1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c10">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b2">A2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c9">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b5">B2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c11">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b8">C2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b3">A3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b6">B3</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b9">C3</font> holds <br/><font color="Maroon" title="c11">c3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b9">C3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c12">A1</font>, <font color="Maroon" title="c13">A2</font>, <font color="Maroon" title="c14">A3</font>, <font color="Maroon" title="c15">B1</font>, <font color="Maroon" title="c16">B2</font>, <font color="Maroon" title="c17">B3</font>, <font color="Maroon" title="c18">C1</font>, <font color="Maroon" title="c19">C2</font>, <font color="Maroon" title="c20">C3</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a>  &amp; <font color="Maroon" title="c14">A3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">B3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">A3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">B3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c12">A1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c10">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c15">B1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c11">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c18">C1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c10">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c13">A2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c9">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c16">B2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c11">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c19">C2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c14">A3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c17">B3</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c20">C3</font> implies <font color="Maroon" title="c11">c3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">C3</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:27"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a> 
 <span class="kw">and </span><br/><a NAME="E3:27"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_different</a> 
 <span class="kw">and </span><br/><a NAME="E4:27"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
<font color="Maroon" title="c14">A3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">B3</font>
 <span class="kw">and </span><br/><a NAME="E5:27"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">A3</font>
 <span class="kw">and </span><br/><a NAME="E6:27"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">B3</font>
 <span class="kw">and </span><br/><a NAME="E7:27"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c12">A1</font>
 <span class="kw">and </span><br/><a NAME="E8:27"/><span class="lab"><font color="Green" title="E25">A8</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c10">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c15">B1</font>
 <span class="kw">and </span><br/><a NAME="E9:27"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c11">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c18">C1</font>
 <span class="kw">and </span><br/><a NAME="E10:27"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c10">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c13">A2</font>
 <span class="kw">and </span><br/><a NAME="E11:27"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c9">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c16">B2</font>
 <span class="kw">and </span><br/><a NAME="E12:27"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c11">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c19">C2</font>
 <span class="kw">and </span><br/><a NAME="E13:27"/><span class="lab"><font color="Green" title="E30">A13</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c14">A3</font>
 <span class="kw">and </span><br/><a NAME="E14:27"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c17">B3</font>
 <span class="kw">and </span><br/><a NAME="E15:27"/><span class="lab"><font color="Green" title="E32">A15</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c20">C3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c11">c3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">C3</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c21">o9</font> = <font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c22">a19</font> = <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c23">a29</font> = <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c24">a39</font> = <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c25">b19</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c26">b29</font> = <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c27">b39</font> = <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c28">c19</font> = <font color="Maroon" title="c9">c1</font>, <font color="Maroon" title="c29">c29</font> = <font color="Maroon" title="c10">c2</font>, <font color="Maroon" title="c30">c39</font> = <font color="Maroon" title="c11">c3</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">CPS</font> ;<br/>
<a NAME="E17:27"/><span class="lab"><font color="Green" title="E33">A16</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">A3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:27"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E18:27"/><span class="lab"><font color="Green" title="E34">A17</font></span>: 
<font color="Maroon" title="c11">c3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E19:27"/>
( <font color="Maroon" title="c3">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">C1</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">C1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E20:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A18</font></span>: 
<font color="Maroon" title="c22">a19</font>,<font color="Maroon" title="c26">b29</font>,<font color="Maroon" title="c30">c39</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="#E18:27"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E21:27"/><span class="lab"><font color="Green" title="E36">A19</font></span>: 
<font color="Maroon" title="c9">c1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">A1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E22:27"/><span class="lab"><font color="Green" title="E37">A20</font></span>: 
( <font color="Maroon" title="c21">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">b39</font> &amp; <font color="Maroon" title="c26">b29</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">b39</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E23:27"/><span class="lab"><font color="Green" title="E38">A21</font></span>: 
( <font color="Maroon" title="c23">a29</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">a39</font> &amp; <font color="Maroon" title="c22">a19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">a29</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E24:27"/><span class="lab"><font color="Green" title="E39">A22</font></span>: 
( <font color="Maroon" title="c8">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">A2</font> &amp; <font color="Maroon" title="c10">c2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">A2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:27"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E25:27"/><span class="lab"><font color="Green" title="E40">A23</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:27"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E26:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A24</font></span>: 
<font color="Maroon" title="c22">a19</font>,<font color="Maroon" title="c27">b39</font>,<font color="Maroon" title="c29">c29</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="#E24:27"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E27:27"/><span class="lab"><font color="Green" title="E42">A25</font></span>: 
( <font color="Maroon" title="c25">b19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">b29</font> &amp; <font color="Maroon" title="c25">b19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">b39</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E28:27"/><span class="lab"><font color="Green" title="E43">A26</font></span>: 
<font color="Maroon" title="c8">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">A1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E29:27"/><span class="lab"><font color="Green" title="E44">A27</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">B3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E30:27"/><span class="lab"><font color="Green" title="E45">A28</font></span>: 
not <font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c22">a19</font>,<font color="Maroon" title="c25">b19</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:27_1"/><span class="lab"><font color="Green" title="E46">A29</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:27_1"/>
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c22">a19</font>,<font color="Maroon" title="c25">b19</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"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c31">K</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E4:27_1"/><span class="lab"><font color="Green" title="E47">A30</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c31">K</font>
 <span class="kw">and </span><br/><a NAME="E5:27_1"/><span class="lab"><font color="Green" title="E48">A31</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c31">K</font>
 <span class="kw">and </span><br/><a NAME="E6:27_1"/><span class="lab"><font color="Green" title="E49">A32</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c31">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E7:27_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E8:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c31">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">A3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E17:27"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="txt" href="#E4:27_1"><span class="lab"><font color="Green" title="E47">A30</font></span></a>, <a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:27_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E29:27"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="txt" href="#E4:27_1"><span class="lab"><font color="Green" title="E47">A30</font></span></a>, <a class="txt" href="#E5:27_1"><span class="lab"><font color="Green" title="E48">A31</font></span></a>, <a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E46">A29</font></span></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</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="E31:27"/><span class="lab"><font color="Green" title="E46">A33</font></span>: 
<font color="Maroon" title="c11">c3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:27"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E32:27"/>
( <font color="Maroon" title="c4">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">C2</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">C2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:27"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E33:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A34</font></span>: 
<font color="Maroon" title="c25">b19</font>,<font color="Maroon" title="c23">a29</font>,<font color="Maroon" title="c30">c39</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="#E31:27"><span class="lab"><font color="Green" title="E46">A33</font></span></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E34:27"/><span class="lab"><font color="Green" title="E48">A35</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">B1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:27"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E35:27"/><span class="lab"><font color="Green" title="E49">A36</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">A3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:27"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E36:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A37</font></span>: 
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c25">b19</font>,<font color="Maroon" title="c26">b29</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="#E5:27"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E17:27"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E37:27"/><span class="lab"><font color="Green" title="E51">A38</font></span>: 
( <font color="Maroon" title="c5">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">B2</font> &amp; <font color="Maroon" title="c9">c1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">B2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:27"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E38:27"/><span class="lab"><font color="Green" title="E52">A39</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">B2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:27"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E39:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A40</font></span>: 
<font color="Maroon" title="c24">a39</font>,<font color="Maroon" title="c26">b29</font>,<font color="Maroon" title="c28">c19</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="#E37:27"><span class="lab"><font color="Green" title="E51">A38</font></span></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E40:27"/><span class="lab"><font color="Green" title="E54">A41</font></span>: 
<font color="Maroon" title="c8">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">A3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:27"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E41:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A42</font></span>: 
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c25">b19</font>,<font color="Maroon" title="c27">b39</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="#E5:27"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E17:27"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E42:27"/><span class="lab"><font color="Green" title="E56">A43</font></span>: 
( <font color="Maroon" title="c22">a19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">a39</font> &amp; <font color="Maroon" title="c21">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">b29</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E43:27"/><span class="lab"><font color="Green" title="E57">A44</font></span>: 
( <font color="Maroon" title="c21">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">a29</font> &amp; <font color="Maroon" title="c21">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">a39</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E44:27"/><span class="lab"><font color="Green" title="E58">A45</font></span>: 
<font color="Maroon" title="c10">c2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">B1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:27"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E45:27"/><span class="lab"><font color="Green" title="E59">A46</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">A1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E46:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A47</font></span>: 
<font color="Maroon" title="c23">a29</font>,<font color="Maroon" title="c27">b39</font>,<font color="Maroon" title="c28">c19</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="#E28:27"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="txt" href="#E21:27"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E47:27"/><span class="lab"><font color="Green" title="E61">A48</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E48:27"/><span class="lab"><font color="Green" title="E62">A49</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E49:27"/><span class="lab"><font color="Green" title="E63">A50</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E50:27"/><span class="lab"><font color="Green" title="E64">A51</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">B1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:27"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E51:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A52</font></span>: 
<font color="Maroon" title="c24">a39</font>,<font color="Maroon" title="c25">b19</font>,<font color="Maroon" title="c29">c29</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="#E34:27"><span class="lab"><font color="Green" title="E48">A35</font></span></a>, <a class="txt" href="#E44:27"><span class="lab"><font color="Green" title="E58">A45</font></span></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E52:27"/><span class="lab"><font color="Green" title="E66">A53</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">B3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E53:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A54</font></span>: 
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c22">a19</font>,<font color="Maroon" title="c24">a39</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="#E6:27"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E29:27"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E54:27"/><span class="lab"><font color="Green" title="E68">A55</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">B3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E55:27"/><span class="kw">then </span>
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c22">a19</font>,<font color="Maroon" title="c23">a29</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="#E6:27"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E29:27"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E56:27"/><span class="kw">then </span>
<font color="Maroon" title="c28">c19</font>,<font color="Maroon" title="c29">c29</font>,<font color="Maroon" title="c30">c39</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="#E1:27"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E43:27"><span class="lab"><font color="Green" title="E57">A44</font></span></a>, <a class="txt" href="#E23:27"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="txt" href="#E42:27"><span class="lab"><font color="Green" title="E56">A43</font></span></a>, <a class="txt" href="#E22:27"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E27:27"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E30:27"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E53:27"><span class="lab"><font color="Green" title="E67">A54</font></span></a>, <a class="txt" href="#E36:27"><span class="lab"><font color="Green" title="E50">A37</font></span></a>, <a class="txt" href="#E41:27"><span class="lab"><font color="Green" title="E55">A42</font></span></a>, <a class="txt" href="#E20:27"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="txt" href="#E33:27"><span class="lab"><font color="Green" title="E47">A34</font></span></a>, <a class="txt" href="#E26:27"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="#E51:27"><span class="lab"><font color="Green" title="E65">A52</font></span></a>, <a class="txt" href="#E46:27"><span class="lab"><font color="Green" title="E60">A47</font></span></a>, <a class="txt" href="#E39:27"><span class="lab"><font color="Green" title="E53">A40</font></span></a></span>;<br/>
<a NAME="E57:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A56</font></span>: 
 ex <font color="Olive" title="b1">K</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span> st <br/>( <font color="Maroon" title="c9">c1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c10">c2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c11">c3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#T14" target="_self" title="INCPROJ:th.14">Th14</a></span>;<br/>
<a NAME="E58:27"/><span class="lab"><font color="Green" title="E70">A57</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D6" title="ZFMISC_1:def.6">ZFMISC_1:def 6</a></span>;<br/>
<a NAME="E59:27"/><span class="lab"><font color="Green" title="E71">A58</font></span>: 
<font color="Maroon" title="c9">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">c2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_2"/><span class="lab"><font color="Green" title="E72">A59</font></span>: 
not <font color="Maroon" title="c9">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">c2</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="E2:27_2"/>
not <font color="Maroon" title="c5">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">A3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E58:27"><span class="lab"><font color="Green" title="E70">A57</font></span></a>, <a class="txt" href="#E52:27"><span class="lab"><font color="Green" title="E66">A53</font></span></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></span>;<br/>
<a NAME="E3:27_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">B1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">B2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:27"><span class="lab"><font color="Green" title="E61">A48</font></span></a>, <a class="txt" href="#E34:27"><span class="lab"><font color="Green" title="E48">A35</font></span></a>, <a class="txt" href="#E50:27"><span class="lab"><font color="Green" title="E64">A51</font></span></a>, <a class="txt" href="#E38:27"><span class="lab"><font color="Green" title="E52">A39</font></span></a>, <a class="txt" href="#E17:27"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="txt" href="#E35:27"><span class="lab"><font color="Green" title="E49">A36</font></span></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></span>;<br/>
<a NAME="E4:27_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A60</font></span>: 
<font color="Maroon" title="c9">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:27"><span class="lab"><font color="Green" title="E48">A35</font></span></a>, <a class="txt" href="#E44:27"><span class="lab"><font color="Green" title="E58">A45</font></span></a>, <a class="txt" href="#E37:27"><span class="lab"><font color="Green" title="E51">A38</font></span></a>, <a class="txt" href="#E1:27_2"><span class="lab"><font color="Green" title="E72">A59</font></span></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></span>;<br/>
<a NAME="E5:27_2"/>
not <font color="Maroon" title="c8">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">B3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E49:27"><span class="lab"><font color="Green" title="E63">A50</font></span></a>, <a class="txt" href="#E40:27"><span class="lab"><font color="Green" title="E54">A41</font></span></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></span>;<br/>
<a NAME="E6:27_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:27"><span class="lab"><font color="Green" title="E62">A49</font></span></a>, <a class="txt" href="#E45:27"><span class="lab"><font color="Green" title="E59">A46</font></span></a>, <a class="txt" href="#E28:27"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="txt" href="#E25:27"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E29:27"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="txt" href="#E54:27"><span class="lab"><font color="Green" title="E68">A55</font></span></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></span>;<br/>
<a NAME="E7:27_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:27"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="txt" href="#E21:27"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E24:27"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E1:27_2"><span class="lab"><font color="Green" title="E72">A59</font></span></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:27_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E49:27"><span class="lab"><font color="Green" title="E63">A50</font></span></a>, <a class="txt" href="#E40:27"><span class="lab"><font color="Green" title="E54">A41</font></span></a>, <a class="txt" href="#E52:27"><span class="lab"><font color="Green" title="E66">A53</font></span></a>, <a class="txt" href="#E4:27_2"><span class="lab"><font color="Green" title="E73">A60</font></span></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</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="E60:27"/>
( <font color="Maroon" title="c9">c1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">C3</font> &amp; <font color="Maroon" title="c10">c2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">C3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:27"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E61:27"/>
<font color="Maroon" title="c11">c3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">C3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:27"><span class="lab"><font color="Green" title="E71">A58</font></span></a>, <a class="txt" href="#E57:27"><span class="lab"><font color="Green" title="E69">A56</font></span></a>, <a class="ref" href="incproj.html#T12" target="_self" title="INCPROJ:th.12">Th12</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>
