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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>



















<b>assume </b><b>that </b><br/><a NAME="E1:63"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> &amp; not <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> is  not   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> )
 <b>and </b><br/><a NAME="E2:63"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>3</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>4</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>5</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_1"/>
( <font color="Maroon">c<sub>3</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>5</sub></font> is    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> )
 ;<br/><a NAME="E2:63_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="afproj.html#E1:63"><i><font color="Green">E56</font></i></a>, <a class="txt" href="afproj.html#E67"><i><font color="Green">Lemma54</font></i></a></i>;<br/><b>hence </b><a NAME="E3:63_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:63"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="afproj.html#E1:63"><i><font color="Green">E56</font></i></a>, <a class="txt" href="afproj.html#E2:63"><i><font color="Green">E57</font></i></a>, <a class="txt" href="afproj.html#E67"><i><font color="Green">Lemma54</font></i></a></i>;<br/>


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