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<div class="add">

<b>let </b><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being  <a href="ortsp_1.html#NM1" title="ORTSP_1:NM.1">OrtSp</a> of <font color="Maroon" title="c4">F</font><br/> for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font>  st not <font color="Olive" title="b3">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Olive" title="b3">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Olive" title="b3">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  holds <br/><span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b4">x</font>,<font color="Olive" title="b3">p</font>,<font color="Olive" title="b5">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b5">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b5">y</font>,<font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">x</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">S</font> be   <a href="ortsp_1.html#NM1" title="ORTSP_1:NM.1">OrtSp</a> of <font color="Maroon" title="c4">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</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="b2">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Olive" title="b2">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Olive" title="b2">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  holds <br/><span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b3">x</font>,<font color="Olive" title="b2">p</font>,<font color="Olive" title="b4">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b4">y</font>,<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">x</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">p</font>, <font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c9">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  implies <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> )</span><br/>











<b>set </b><font color="Maroon" title="c10">0F</font> =  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font>;<br/>
<b>set </b><font color="Maroon" title="c11">1F</font> =  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c4">F</font>;<br/>
<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E31">A1</font></i>: 
( not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span></span><br/>

<a NAME="E2:35"/><b>then </b><i><font color="Green" title="E32">A2</font></i>: 
( not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c6">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c8">x</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c9">y</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  )
 
<b>by </b><i><a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></i>;<br/>
<div><i><font color="Green" title="E33">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:35_1"/>
<font color="Maroon" title="c8">x</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span></span><br/><a NAME="E2:35_1"/><b>then </b>
( <font color="Maroon" title="c8">x</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Maroon" title="c9">y</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  )
 <b>by </b><i><a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></i>;<br/><a NAME="E3:35_1"/><b>then </b>
(  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> &amp;  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> )
 <b>by </b><i><a class="txt" href="ortsp_1.html#E2:35"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="ortsp_1.html#T33" target="_self" title="ORTSP_1:th.33">Th33</a></i>;<br/><a NAME="E4:35_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> &amp; <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> )
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>;<br/><b>hence </b><a NAME="E5:35_1"/>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:35_2"/><i><font color="Green" title="E34">A4</font></i>: 
not <font color="Maroon" title="c8">x</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span></span><br/><a NAME="E2:35_2"/><b>then </b><i><font color="Green" title="E35">A5</font></i>: 
( not <font color="Maroon" title="c8">x</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c9">y</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  )
 <b>by </b><i><a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></i>;<br/><a NAME="E3:35_2"/>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</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="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:35"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="ortsp_1.html#T34" target="_self" title="ORTSP_1:th.34">Th34</a></i>;<br/><a NAME="E4:35_2"/><b>then </b>
<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="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E2:35"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="ortsp_1.html#E1:35_2"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="ortsp_1.html#T37" target="_self" title="ORTSP_1:th.37">Th37</a></i>;<br/><a NAME="E5:35_2"/><b>then </b><i><font color="Green" title="E36">A6</font></i>: 
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>;<br/><a NAME="E6:35_2"/>
 <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:35"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="ortsp_1.html#T33" target="_self" title="ORTSP_1:th.33">Th33</a></i>;<br/><a NAME="E7:35_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E5:35_2"><i><font color="Green" title="E36">A6</font></i></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></i>;<br/><a NAME="E8:35_2"/><b>then </b>
 <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</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="c9">y</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>;<br/><a NAME="E9:35_2"/><b>then </b>
 <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>;<br/><a NAME="E10:35_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E2:35"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="ortsp_1.html#E2:35_2"><i><font color="Green" title="E35">A5</font></i></a>, <a class="ref" href="ortsp_1.html#T35" target="_self" title="ORTSP_1:th.35">Th35</a></i>;<br/><a NAME="E11:35_2"/><b>then </b><i><font color="Green" title="E37">A7</font></i>: 
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <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="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>;<br/><a NAME="E12:35_2"/>
 <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E2:35"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="ortsp_1.html#E2:35_2"><i><font color="Green" title="E35">A5</font></i></a>, <a class="ref" href="ortsp_1.html#T33" target="_self" title="ORTSP_1:th.33">Th33</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c4">F</font></span>)</span>
<b>by </b><i><a class="txt" href="ortsp_1.html#E11:35_2"><i><font color="Green" title="E37">A7</font></i></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></i>
<br/>.= 
<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">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>
;<br/><b>hence </b><a NAME="E14:35_2"/>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E2:35"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="ortsp_1.html#E1:35_2"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="ortsp_1.html#T35" target="_self" title="ORTSP_1:th.35">Th35</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:35"/>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E3:35"><i><font color="Green" title="E33">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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