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<b>let </b><font color="Maroon" title="c10">IT1</font>, <font color="Maroon" title="c11">IT2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">F</font>;<br/>

<b>thus </b><a NAME="E1:36_1_2"/>
(  ex <font color="Olive" title="b1">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font> st <br/>( not <font color="Olive" title="b1">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">a</font> &amp; not <font color="Olive" title="b1">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">x</font> ) &amp; ( for <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>  st not <font color="Olive" title="b1">q</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">a</font> &amp; not <font color="Olive" title="b1">q</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">x</font> holds <br/><font color="Maroon" title="c10">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Olive" title="b1">q</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">q</font>,<font color="Maroon" title="c7">y</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>  st not <font color="Olive" title="b1">q</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">a</font> &amp; not <font color="Olive" title="b1">q</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">x</font> holds <br/><font color="Maroon" title="c11">IT2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Olive" title="b1">q</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">q</font>,<font color="Maroon" title="c7">y</font></span>)</span> ) implies <font color="Maroon" title="c10">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">IT2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_2_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c12">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font><b> such that </b><a NAME="E1:36_1_2_1"/><i><font color="Green" title="E32">A3</font></i>: 
( not <font color="Maroon" title="c12">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">a</font> &amp; not <font color="Maroon" title="c12">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">x</font> )
 ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:36_1_2_1"/><i><font color="Green" title="E33">A4</font></i>: 
for <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>  st not <font color="Olive" title="b1">q</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">a</font> &amp; not <font color="Olive" title="b1">q</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">x</font> holds <br/><font color="Maroon" title="c10">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Olive" title="b1">q</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">q</font>,<font color="Maroon" title="c7">y</font></span>)</span>
 <b>and </b><br/><a NAME="E3:36_1_2_1"/><i><font color="Green" title="E34">A5</font></i>: 
for <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>  st not <font color="Olive" title="b1">q</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">a</font> &amp; not <font color="Olive" title="b1">q</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">x</font> holds <br/><font color="Maroon" title="c11">IT2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Olive" title="b1">q</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">q</font>,<font color="Maroon" title="c7">y</font></span>)</span>
 ;<br/>

<b>consider </b><font color="Maroon" title="c13">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font><b> such that </b><br/><a NAME="E5:36_1_2_1"/><i><font color="Green" title="E35">A6</font></i>: 
( not <font color="Maroon" title="c13">r</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">a</font> &amp; not <font color="Maroon" title="c13">r</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">x</font> )
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:36_1_2_1"><i><font color="Green" title="E32">A3</font></i></a></i>;<br/>
<a NAME="E6:36_1_2_1"/>
<font color="Maroon" title="c10">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c13">r</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c13">r</font>,<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c13">r</font>,<font color="Maroon" title="c7">y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ortsp_1.html#E2:36_1_2_1"><i><font color="Green" title="E33">A4</font></i></a>, <a class="txt" href="ortsp_1.html#E5:36_1_2_1"><i><font color="Green" title="E35">A6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:36_1_2_1"/>
<font color="Maroon" title="c10">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">IT2</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E3:36_1_2_1"><i><font color="Green" title="E34">A5</font></i></a>, <a class="txt" href="ortsp_1.html#E5:36_1_2_1"><i><font color="Green" title="E35">A6</font></i></a></i>;<br/>


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

<b>thus </b><a NAME="E2:36_1_2"/>
( ( for <font color="Olive" title="b1">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>  holds <br/>( <font color="Olive" title="b1">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">a</font> or <font color="Olive" title="b1">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">x</font> ) ) &amp; <font color="Maroon" title="c10">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c4">F</font> &amp; <font color="Maroon" title="c11">IT2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c4">F</font> implies <font color="Maroon" title="c10">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">IT2</font> )
 ;<br/>


</div>
