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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="incsp_1.html#NM4" title="INCSP_1:NM.4">IncSpace</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">A</font>, <font color="Olive" title="b2">B</font>, <font color="Olive" title="b3">C</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>  st not <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> is  <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a>  holds <br/> <a href="incsp_1.html#K2" title="INCSP_1:func.2">Plane</a> <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="incsp_1.html#K2" title="INCSP_1:func.2">Plane</a> <font color="Olive" title="b3">C</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> is  <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a>  implies  <a href="incsp_1.html#K2" title="INCSP_1:func.2">Plane</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="incsp_1.html#K2" title="INCSP_1:func.2">Plane</a> <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:83"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
not <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> is  <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="incsp_1.html#K2" title="INCSP_1:func.2">Plane</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="incsp_1.html#K2" title="INCSP_1:func.2">Plane</a> <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span><br/>

<a NAME="E2:83"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A2</font></span>: 
not <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> is  <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T100" title="ENUMSET1:th.100">ENUMSET1:100</a></span>;<br/>
<span class="kw">thus </span> <a href="incsp_1.html#K2" title="INCSP_1:func.2">Plane</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font> = 
 <a href="incsp_1.html#K2" title="INCSP_1:func.2">Plane</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c3">B</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="incsp_1.html#T58" target="_self" title="INCSP_1:th.58">Th58</a></span>
<br/>.= 
 <a href="incsp_1.html#K2" title="INCSP_1:func.2">Plane</a> <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="incsp_1.html#T59" target="_self" title="INCSP_1:th.59">Th59</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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