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<div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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/>











<span class="kw">set </span><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/>
<span class="kw">set </span><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/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:48"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">and </span><br/><a NAME="E2:48"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">and </span><br/><a NAME="E3:48"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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="E4:48"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
not <font color="Maroon" title="c9">y</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></span>;<br/>
<a NAME="E5:48"/><span class="lab"><font color="Green" title="E35">A5</font></span>: 
not <font color="Maroon" title="c8">x</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:48"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E36">A6</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:48_1"/><span class="lab"><font color="Green" title="E37">A7</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E2:48"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="ortsp_1.html#T33" target="_self" title="ORTSP_1:th.33">Th33</a></span>;<br/><span class="kw">assume </span><a NAME="E2:48_1"/><span class="lab"><font color="Green" title="E38">A8</font></span>: 
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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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="E3:48_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A9</font></span>: 
not <font color="Maroon" title="c9">y</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></span>;<br/><a NAME="E4:48_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="c9">y</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E2:48"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="ortsp_1.html#T34" target="_self" title="ORTSP_1:th.34">Th34</a></span>;<br/><a NAME="E5:48_1"/><span class="kw">then </span>
<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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="txt" href="#E2:48_1"><span class="lab"><font color="Green" title="E38">A8</font></span></a>, <a class="ref" href="ortsp_1.html#T37" target="_self" title="ORTSP_1:th.37">Th37</a></span>;<br/><a NAME="E6:48_1"/><span class="kw">then </span>
<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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>;<br/><a NAME="E7:48_1"/><span class="kw">then </span>
<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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48_1"><span class="lab"><font color="Green" title="E37">A7</font></span></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></span>;<br/><a NAME="E8:48_1"/><span class="kw">then </span>
 <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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></span>;<br/><a NAME="E9:48_1"/><span class="kw">then </span>
 <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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>;<br/><a NAME="E10:48_1"/><span class="kw">then </span>
<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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="txt" href="#E3:48_1"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="ortsp_1.html#T35" target="_self" title="ORTSP_1:th.35">Th35</a></span>;<br/><a NAME="E11:48_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A10</font></span>: 
<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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>;<br/><a NAME="E12:48_1"/>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="txt" href="#E3:48_1"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="ortsp_1.html#T33" target="_self" title="ORTSP_1:th.33">Th33</a></span>;<br/><span class="kw">then </span><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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:48_1"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></span>
<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#K8" title="GROUP_1:func.8">*</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></span>
;<br/><span class="kw">hence </span><a NAME="E14:48_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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="txt" href="#E2:48_1"><span class="lab"><font color="Green" title="E38">A8</font></span></a>, <a class="ref" href="ortsp_1.html#T35" target="_self" title="ORTSP_1:th.35">Th35</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:48_2"/><span class="lab"><font color="Green" title="E37">A11</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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="E2:48_2"/><span class="kw">then </span>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="ortsp_1.html#T33" target="_self" title="ORTSP_1:th.33">Th33</a></span>;<br/><a NAME="E3:48_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A12</font></span>: 
<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#K8" title="GROUP_1:func.8">*</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></span>;<br/><a NAME="E4:48_2"/>
<font color="Maroon" title="c9">y</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48_2"><span class="lab"><font color="Green" title="E37">A11</font></span></a>, <a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></span>;<br/><a NAME="E5:48_2"/><span class="kw">then </span>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="ortsp_1.html#T33" target="_self" title="ORTSP_1:th.33">Th33</a></span>;<br/><span class="kw">hence </span><a NAME="E6:48_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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48_2"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E8:48"/>
<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#K8" title="GROUP_1:func.8">*</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#K8" title="GROUP_1:func.8">*</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E6:48"><span class="lab"><font color="Green" title="E36">A6</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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