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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>, <font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>5</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>













<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>assume </b><a NAME="E1:41"/><i><font color="Green">E35</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>
 ;<br/>

<div><i><font color="Green">E36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:41_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E2:41_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="ortsp_1.html#T12" target="_self">Th12</a></i>;<br/><a NAME="E3:41_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="ortsp_1.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E4:41_1"/><b>then </b>
( <font color="Maroon">c<sub>8</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>10</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:41_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="ortsp_1.html#T12" target="_self">Th12</a></i>;<br/><a NAME="E5:41_1"/><b>then </b>
( <font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K2" target="_self">PProJ</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>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> &amp;  <a href="ortsp_1.html#K2" target="_self">PProJ</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 class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <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#E1:41"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ortsp_1.html#T44" target="_self">Th44</a></i>;<br/><b>hence </b><a NAME="E6:41_1"/>
 <a href="ortsp_1.html#K2" target="_self">PProJ</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 class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K2" target="_self">PProJ</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>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:41_2"/>
not <font color="Maroon">c<sub>8</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E2:41_2"/><b>then </b>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="ortsp_1.html#E59"><i><font color="Green">Lemma33</font></i></a>, <a class="ref" href="ortsp_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E3:41_2"/><b>then </b>
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>7</sub></font> &amp; 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>7</sub></font> &amp; not <font color="Olive">b<sub>1</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="ref" href="ortsp_1.html#D2" target="_self">Def2</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E5:41_2"/><i><font color="Green">E37</font></i>: 
( not <font color="Maroon">c<sub>12</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>7</sub></font> &amp; not <font color="Maroon">c<sub>12</sub></font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/><a NAME="E6:41_2"/><i><font color="Green">E38</font></i>: 
 <a href="ortsp_1.html#K2" target="_self">PProJ</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 class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</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>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>12</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>12</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</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>8</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="ortsp_1.html#E5:41_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="ortsp_1.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E7:41_2"/><i><font color="Green">E39</font></i>: 
 <a href="ortsp_1.html#K2" target="_self">PProJ</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>,<font color="Maroon">c<sub>9</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>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>12</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>12</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</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>8</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="ortsp_1.html#E5:41_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="ortsp_1.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E8:41_2"/>
 <a href="ortsp_1.html#K2" target="_self">PProJ</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 class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <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>8</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</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>12</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>12</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E5:41_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="ortsp_1.html#E6:41_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="ortsp_1.html#T25" target="_self">Th25</a></i>;<br/><b>hence </b><a NAME="E9:41_2"/>
 <a href="ortsp_1.html#K2" target="_self">PProJ</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 class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K2" target="_self">PProJ</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>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E7:41_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:41"/>
 <a href="ortsp_1.html#K2" target="_self">PProJ</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 class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K2" target="_self">PProJ</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>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E2:41"><i><font color="Green">E36</font></i></a></i>;<br/>


</div>
