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<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="symsp_1.html#NM1" title="SYMSP_1:NM.1">SymSp</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">q</font>, <font color="Olive" title="b5">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font>  st <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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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#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> &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="b4">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Olive" title="b4">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  holds <br/><span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b5">b</font>,<font color="Olive" title="b4">q</font>,<font color="Olive" title="b3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b5">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b4">q</font>,<font color="Olive" title="b5">b</font>,<font color="Olive" title="b2">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">S</font> be   <a href="symsp_1.html#NM1" title="SYMSP_1:NM.1">SymSp</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">q</font>, <font color="Olive" title="b4">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>  st <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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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#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> &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="b3">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Olive" title="b3">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  holds <br/><span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b4">b</font>,<font color="Olive" title="b3">q</font>,<font color="Olive" title="b2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b1">a</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">q</font>, <font color="Maroon" title="c9">b</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"> ( <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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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#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> &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="c8">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c8">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  implies <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</span> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:54"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
<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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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#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">and </span><br/><a NAME="E2:54"/><span class="lab"><font color="Green" title="E36">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="E3:54"/><span class="lab"><font color="Green" title="E37">A3</font></span>: 
not <font color="Maroon" title="c8">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">and </span><br/><a NAME="E4:54"/><span class="lab"><font color="Green" title="E38">A4</font></span>: 
not <font color="Maroon" title="c8">q</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</span></span><br/>

<div><span class="lab"><font color="Green" title="E39">A5</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:54_1"/><span class="lab"><font color="Green" title="E40">A6</font></span>: 
<font color="Maroon" title="c8">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">and </span><br/><a NAME="E2:54_1"/><span class="lab"><font color="Green" title="E41">A7</font></span>: 
<font color="Maroon" title="c9">b</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</span></span><br/><a NAME="E3:54_1"/>
not <font color="Maroon" title="c9">b</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="#E4:54"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></span>;<br/><a NAME="E4:54_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A8</font></span>: 
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54_1"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="ref" href="symsp_1.html#T32" target="_self" title="SYMSP_1:th.32">Th32</a></span>;<br/><a NAME="E5:54_1"/><span class="lab"><font color="Green" title="E43">A9</font></span>: 
not <font color="Maroon" title="c8">q</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="#E3:54"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E1:54_1"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="ref" href="symsp_1.html#T14" target="_self" title="SYMSP_1:th.14">Th14</a></span>;<br/><a NAME="E6:54_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A10</font></span>: 
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c9">b</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:54"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="symsp_1.html#T40" target="_self" title="SYMSP_1:th.40">Th40</a></span>;<br/><a NAME="E7:54_1"/><span class="lab"><font color="Green" title="E45">A11</font></span>: 
<font color="Maroon" title="c6">a</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="#E1:54"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="symsp_1.html#T25" target="_self" title="SYMSP_1:th.25">Th25</a></span>;<br/><a NAME="E8:54_1"/><span class="lab"><font color="Green" title="E46">A12</font></span>: 
not <font color="Maroon" title="c6">a</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="#E2:54"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></span>;<br/><a NAME="E9:54_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A13</font></span>: 
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:54_1"><span class="lab"><font color="Green" title="E45">A11</font></span></a>, <a class="ref" href="symsp_1.html#T32" target="_self" title="SYMSP_1:th.32">Th32</a></span>;<br/><a NAME="E10:54_1"/>
not <font color="Maroon" title="c6">a</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="#E8:54_1"><span class="lab"><font color="Green" title="E46">A12</font></span></a>, <a class="txt" href="#E7:54_1"><span class="lab"><font color="Green" title="E45">A11</font></span></a>, <a class="ref" href="symsp_1.html#T14" target="_self" title="SYMSP_1:th.14">Th14</a></span>;<br/><a NAME="E11:54_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A14</font></span>: 
not <font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</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="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></span>;<br/><a NAME="E12:54_1"/><span class="lab"><font color="Green" title="E49">A15</font></span>: 
not <font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</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="#E5:54_1"><span class="lab"><font color="Green" title="E43">A9</font></span></a>, <a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></span>;<br/><a NAME="E13:54_1"/><span class="kw">then </span>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c6">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:54_1"><span class="lab"><font color="Green" title="E48">A14</font></span></a>, <a class="ref" href="symsp_1.html#T40" target="_self" title="SYMSP_1:th.40">Th40</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:54_1"><span class="lab"><font color="Green" title="E47">A13</font></span></a>, <a class="txt" href="#E4:54_1"><span class="lab"><font color="Green" title="E42">A8</font></span></a>, <a class="txt" href="#E6:54_1"><span class="lab"><font color="Green" title="E44">A10</font></span></a>, <a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c6">a</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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</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="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c6">a</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"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c9">b</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"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T42" title="VECTSP_1:th.42">VECTSP_1:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c9">b</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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:54"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E5:54_1"><span class="lab"><font color="Green" title="E43">A9</font></span></a>, <a class="ref" href="symsp_1.html#T37" target="_self" title="SYMSP_1:th.37">Th37</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </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/>.= 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:54_1"><span class="lab"><font color="Green" title="E48">A14</font></span></a>, <a class="txt" href="#E12:54_1"><span class="lab"><font color="Green" title="E49">A15</font></span></a>, <a class="ref" href="symsp_1.html#T37" target="_self" title="SYMSP_1:th.37">Th37</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E2:54_1"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="txt" href="#E7:54_1"><span class="lab"><font color="Green" title="E45">A11</font></span></a>, <a class="ref" href="symsp_1.html#T33" target="_self" title="SYMSP_1:th.33">Th33</a></span>
;<br/><span class="kw">hence </span><a NAME="E15:54_1"/>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</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><span class="lab"><font color="Green" title="E40">A16</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="54_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:54_2"/><span class="lab"><font color="Green" title="E41">A17</font></span>: 
not <font color="Maroon" title="c9">b</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</span></span><br/><a NAME="E2:54_2"/><span class="lab"><font color="Green" title="E42">A18</font></span>: 
not <font color="Maroon" title="c9">b</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="#E4:54"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></span>;<br/><a NAME="E3:54_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A19</font></span>: 
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">q</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_2"><span class="lab"><font color="Green" title="E41">A17</font></span></a>, <a class="ref" href="symsp_1.html#T40" target="_self" title="SYMSP_1:th.40">Th40</a></span>;<br/><a NAME="E4:54_2"/><span class="lab"><font color="Green" title="E44">A20</font></span>: 
not <font color="Maroon" title="c6">a</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="#E2:54"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></span>;<br/><a NAME="E5:54_2"/><span class="lab"><font color="Green" title="E45">A21</font></span>: 
not <font color="Maroon" title="c6">a</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="#E1:54_2"><span class="lab"><font color="Green" title="E41">A17</font></span></a>, <a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></span>;<br/><a NAME="E6:54_2"/><span class="kw">then </span>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:54_2"><span class="lab"><font color="Green" title="E44">A20</font></span></a>, <a class="ref" href="symsp_1.html#T40" target="_self" title="SYMSP_1:th.40">Th40</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</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></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54_2"><span class="lab"><font color="Green" title="E43">A19</font></span></a>, <a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</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="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</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"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">q</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"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</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></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T42" title="VECTSP_1:th.42">VECTSP_1:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">q</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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_2"><span class="lab"><font color="Green" title="E41">A17</font></span></a>, <a class="txt" href="#E2:54_2"><span class="lab"><font color="Green" title="E42">A18</font></span></a>, <a class="ref" href="symsp_1.html#T37" target="_self" title="SYMSP_1:th.37">Th37</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</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"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</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>
<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/>.= 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</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"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:54_2"><span class="lab"><font color="Green" title="E45">A21</font></span></a>, <a class="txt" href="#E4:54_2"><span class="lab"><font color="Green" title="E44">A20</font></span></a>, <a class="ref" href="symsp_1.html#T37" target="_self" title="SYMSP_1:th.37">Th37</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:54_2"/>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</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="54_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:54_3"/><span class="lab"><font color="Green" title="E41">A22</font></span>: 
not <font color="Maroon" title="c8">q</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</span></span><br/><a NAME="E2:54_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A23</font></span>: 
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">b</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:54"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="symsp_1.html#T40" target="_self" title="SYMSP_1:th.40">Th40</a></span>;<br/><a NAME="E3:54_3"/><span class="lab"><font color="Green" title="E43">A24</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">by</span> <span class="lab"><a class="txt" href="#E1:54_3"><span class="lab"><font color="Green" title="E41">A22</font></span></a>, <a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></span>;<br/><a NAME="E4:54_3"/><span class="kw">then </span>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="symsp_1.html#T40" target="_self" title="SYMSP_1:th.40">Th40</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54_3"><span class="lab"><font color="Green" title="E42">A23</font></span></a>, <a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</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="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</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"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">b</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"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T42" title="VECTSP_1:th.42">VECTSP_1:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">b</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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:54"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E1:54_3"><span class="lab"><font color="Green" title="E41">A22</font></span></a>, <a class="ref" href="symsp_1.html#T37" target="_self" title="SYMSP_1:th.37">Th37</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </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/>.= 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E3:54_3"><span class="lab"><font color="Green" title="E43">A24</font></span></a>, <a class="ref" href="symsp_1.html#T37" target="_self" title="SYMSP_1:th.37">Th37</a></span>
;<br/><span class="kw">hence </span><a NAME="E6:54_3"/>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</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="E8:54"/>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">q</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:54"><span class="lab"><font color="Green" title="E40">A16</font></span></a>, <a class="txt" href="#E5:54"><span class="lab"><font color="Green" title="E39">A5</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/>


</div>
