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<b>thus </b><a NAME="E1:36_1_1"/>
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>5</sub></font> st <br/>( not <font color="Olive">b<sub>1</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font> &amp; not <font color="Olive">b<sub>1</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>6</sub></font> ) implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>4</sub></font> st <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>5</sub></font> st not <font color="Olive">b<sub>2</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font> &amp; not <font color="Olive">b<sub>2</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>6</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Olive">b<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>5</sub></font><b> such that </b><a NAME="E1:36_1_1_1"/><i><font color="Green">E32</font></i>: 
( not <font color="Maroon">c<sub>10</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font> &amp; not <font color="Maroon">c<sub>10</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<b>take </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
;<br/>

<b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>5</sub></font>;<br/>

<b>assume </b><a NAME="E2:36_1_1_1"/>
( not <font color="Maroon">c<sub>11</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font> &amp; not <font color="Maroon">c<sub>11</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<b>hence </b><a NAME="E3:36_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:36"><i><font color="Green">E31</font></i></a>, <a class="txt" href="ortsp_1.html#E1:36_1_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="ortsp_1.html#T39" target="_self">Th39</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:36_1_1"/>
( ( for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>5</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>6</sub></font> ) ) implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>4</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>


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