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<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="ortsp_1.html#NM1">OrtSp</a> of <font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>5</sub></font>;<br/>









<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<div><i><font color="Green">E24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1"/><i><font color="Green">E25</font></i>: 
( not <font color="Maroon">c<sub>6</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><a NAME="E2:28_1"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K6">-</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>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="ortsp_1.html#T24" target="_self">Th24</a></i>;<br/><a NAME="E3:28_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:28_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>;<br/><a NAME="E4:28_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T25">RLVECT_1:25</a></i>;<br/><a NAME="E5:28_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T59">VECTSP_1:59</a></i>;<br/><a NAME="E6:28_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D11">RLVECT_1:def 11</a></i>;<br/><b>hence </b><a NAME="E7:28_1"/>
 <a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:28_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="ortsp_1.html#E2:28_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="ortsp_1.html#T20" target="_self">Th20</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_2"/>
( not <font color="Maroon">c<sub>6</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</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/><a NAME="E2:28_2"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="ortsp_1.html#T24" target="_self">Th24</a></i>;<br/><a NAME="E3:28_2"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T59">VECTSP_1:59</a></i>;<br/><a NAME="E4:28_2"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D11">RLVECT_1:def 11</a></i>;<br/><a NAME="E5:28_2"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T25">RLVECT_1:25</a></i>;<br/><b>hence </b><a NAME="E6:28_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:28"/>
( not <font color="Maroon">c<sub>6</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font> implies ( <font color="Maroon">c<sub>8</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font> iff  <a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font> ) )
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:28"><i><font color="Green">E24</font></i></a></i>;<br/>


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