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<span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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">b</font>, <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">q</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="b4">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp;  not <font color="Olive" title="b5">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp;  not <font color="Olive" title="b5">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="b4">p</font>,<font color="Olive" title="b5">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="b3">b</font>,<font color="Olive" title="b5">q</font>,<font color="Olive" title="b4">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="b4">p</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">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="b5">q</font>,<font color="Olive" title="b3">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>  st <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="b1">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="b2">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="b1">a</font>,<font color="Olive" title="b2">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="b2">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">b</font>, <font color="Maroon" title="c8">p</font>, <font color="Maroon" title="c9">q</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c8">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp;  not <font color="Maroon" title="c9">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp;  not <font color="Maroon" title="c9">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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">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="E1:41"/><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="E2:41"/><span class="lab"><font color="Green" title="E36">A2</font></span>: 
 not <font color="Maroon" title="c8">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">and </span><br/><a NAME="E3:41"/><span class="lab"><font color="Green" title="E37">A3</font></span>: 
 not <font color="Maroon" title="c9">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">and </span><br/><a NAME="E4:41"/><span class="lab"><font color="Green" title="E38">A4</font></span>: 
 not <font color="Maroon" title="c9">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="41_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Maroon" title="c7">b</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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> )</span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:41_1"/><span class="lab"><font color="Green" title="E40">A6</font></span>: 
<font color="Maroon" title="c9">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">and </span><br/><a NAME="E2:41_1"/><span class="lab"><font color="Green" title="E41">A7</font></span>: 
<font color="Maroon" title="c7">b</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)</span>)</span></span><br/><a NAME="E3:41_1"/>
 not <font color="Maroon" title="c7">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="#E4:41"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="symsp_1.html#T2" target="_self" onmouseover="rs('symsp_1/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E4:41_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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">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="#E2:41_1"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="ref" href="symsp_1.html#T19" target="_self" onmouseover="rs('symsp_1/T19')" onmouseout="rh()">Th19</a></span>;<br/><a NAME="E5:41_1"/><span class="lab"><font color="Green" title="E43">A9</font></span>: 
 not <font color="Maroon" title="c9">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="#E3:41"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E1:41_1"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="ref" href="symsp_1.html#T4" target="_self" onmouseover="rs('symsp_1/T4')" onmouseout="rh()">Th4</a></span>;<br/><a NAME="E6:41_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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">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="c9">q</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">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="c7">b</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">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">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="symsp_1.html#T27" target="_self" onmouseover="rs('symsp_1/T27')" onmouseout="rh()">Th27</a></span>;<br/><a NAME="E7:41_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="#E1:41"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="symsp_1.html#T13" target="_self" onmouseover="rs('symsp_1/T13')" onmouseout="rh()">Th13</a></span>;<br/><a NAME="E8:41_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="#E2:41"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="symsp_1.html#T2" target="_self" onmouseover="rs('symsp_1/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E9:41_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="c8">p</font>,<font color="Maroon" title="c9">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="c8">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">q</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:41_1"><span class="lab"><font color="Green" title="E45">A11</font></span></a>, <a class="ref" href="symsp_1.html#T19" target="_self" onmouseover="rs('symsp_1/T19')" onmouseout="rh()">Th19</a></span>;<br/><a NAME="E10:41_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="#E8:41_1"><span class="lab"><font color="Green" title="E46">A12</font></span></a>, <a class="txt" href="#E7:41_1"><span class="lab"><font color="Green" title="E45">A11</font></span></a>, <a class="ref" href="symsp_1.html#T4" target="_self" onmouseover="rs('symsp_1/T4')" onmouseout="rh()">Th4</a></span>;<br/><a NAME="E11:41_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A14</font></span>: 
 not <font color="Maroon" title="c8">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#T2" target="_self" onmouseover="rs('symsp_1/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E12:41_1"/><span class="lab"><font color="Green" title="E49">A15</font></span>: 
 not <font color="Maroon" title="c8">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="#E5:41_1"><span class="lab"><font color="Green" title="E43">A9</font></span></a>, <a class="ref" href="symsp_1.html#T2" target="_self" onmouseover="rs('symsp_1/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E13:41_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="c8">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">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="c8">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">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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">q</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">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="#E11:41_1"><span class="lab"><font color="Green" title="E48">A14</font></span></a>, <a class="ref" href="symsp_1.html#T27" target="_self" onmouseover="rs('symsp_1/T27')" onmouseout="rh()">Th27</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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c9">q</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">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="c8">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">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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">q</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">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="c7">b</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">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">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:41_1"><span class="lab"><font color="Green" title="E47">A13</font></span></a>, <a class="txt" href="#E4:41_1"><span class="lab"><font color="Green" title="E42">A8</font></span></a>, <a class="txt" href="#E6:41_1"><span class="lab"><font color="Green" title="E44">A10</font></span></a>, <a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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">q</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">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="c8">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">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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">q</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">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="c7">b</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">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">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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">q</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">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="c9">q</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">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="c7">b</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">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">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">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">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T10" onmouseover="rs('vectsp_1/T10')" onmouseout="rh()">VECTSP_1:10</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">q</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">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="c9">q</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">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="c7">b</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">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">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">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">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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">q</font>,<font color="Maroon" title="c7">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="c8">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">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">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">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E5:41_1"><span class="lab"><font color="Green" title="E43">A9</font></span></a>, <a class="ref" href="symsp_1.html#T24" target="_self" onmouseover="rs('symsp_1/T24')" onmouseout="rh()">Th24</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">q</font>,<font color="Maroon" title="c7">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="c8">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">q</font>,<font color="Maroon" title="c7">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="c8">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">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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">q</font>,<font color="Maroon" title="c7">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="c8">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="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:41_1"><span class="lab"><font color="Green" title="E48">A14</font></span></a>, <a class="txt" href="#E12:41_1"><span class="lab"><font color="Green" title="E49">A15</font></span></a>, <a class="ref" href="symsp_1.html#T24" target="_self" onmouseover="rs('symsp_1/T24')" onmouseout="rh()">Th24</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">q</font>,<font color="Maroon" title="c7">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E2:41_1"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="txt" href="#E7:41_1"><span class="lab"><font color="Green" title="E45">A11</font></span></a>, <a class="ref" href="symsp_1.html#T20" target="_self" onmouseover="rs('symsp_1/T20')" onmouseout="rh()">Th20</a></span>
;<br/><span class="kw">hence </span><a NAME="E15:41_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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="41_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">b</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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:41_2"/><span class="lab"><font color="Green" title="E41">A17</font></span>: 
 not <font color="Maroon" title="c7">b</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)</span>)</span></span><br/><a NAME="E2:41_2"/><span class="lab"><font color="Green" title="E42">A18</font></span>: 
 not <font color="Maroon" title="c7">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="#E4:41"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="symsp_1.html#T2" target="_self" onmouseover="rs('symsp_1/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E3:41_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="c9">q</font>,<font color="Maroon" title="c7">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="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">q</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c7">b</font>,<font color="Maroon" title="c9">q</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41_2"><span class="lab"><font color="Green" title="E41">A17</font></span></a>, <a class="ref" href="symsp_1.html#T27" target="_self" onmouseover="rs('symsp_1/T27')" onmouseout="rh()">Th27</a></span>;<br/><a NAME="E4:41_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="#E2:41"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="symsp_1.html#T2" target="_self" onmouseover="rs('symsp_1/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E5:41_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="#E1:41_2"><span class="lab"><font color="Green" title="E41">A17</font></span></a>, <a class="ref" href="symsp_1.html#T2" target="_self" onmouseover="rs('symsp_1/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E6:41_2"/><span class="kw">then </span>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> (<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c7">b</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">p</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41_2"><span class="lab"><font color="Green" title="E44">A20</font></span></a>, <a class="ref" href="symsp_1.html#T27" target="_self" onmouseover="rs('symsp_1/T27')" onmouseout="rh()">Th27</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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">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="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">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="c7">b</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">q</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c7">b</font>,<font color="Maroon" title="c9">q</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:41_2"><span class="lab"><font color="Green" title="E43">A19</font></span></a>, <a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">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="c7">b</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">q</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c7">b</font>,<font color="Maroon" title="c9">q</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">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="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">q</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c7">b</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c7">b</font>,<font color="Maroon" title="c9">q</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T10" onmouseover="rs('vectsp_1/T10')" onmouseout="rh()">VECTSP_1:10</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="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">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="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">q</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c7">b</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c7">b</font>,<font color="Maroon" title="c9">q</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c7">b</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c7">b</font>,<font color="Maroon" title="c9">q</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41_2"><span class="lab"><font color="Green" title="E41">A17</font></span></a>, <a class="txt" href="#E2:41_2"><span class="lab"><font color="Green" title="E42">A18</font></span></a>, <a class="ref" href="symsp_1.html#T24" target="_self" onmouseover="rs('symsp_1/T24')" onmouseout="rh()">Th24</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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c7">b</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c9">q</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:41_2"><span class="lab"><font color="Green" title="E45">A21</font></span></a>, <a class="txt" href="#E4:41_2"><span class="lab"><font color="Green" title="E44">A20</font></span></a>, <a class="ref" href="symsp_1.html#T24" target="_self" onmouseover="rs('symsp_1/T24')" onmouseout="rh()">Th24</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:41_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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="41_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:41_3"/><span class="lab"><font color="Green" title="E41">A22</font></span>: 
 not <font color="Maroon" title="c9">q</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)</span>)</span></span><br/><a NAME="E2:41_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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c9">q</font>,<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c7">b</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="symsp_1.html#T27" target="_self" onmouseover="rs('symsp_1/T27')" onmouseout="rh()">Th27</a></span>;<br/><a NAME="E3:41_3"/><span class="lab"><font color="Green" title="E43">A24</font></span>: 
 not <font color="Maroon" title="c8">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="#E1:41_3"><span class="lab"><font color="Green" title="E41">A22</font></span></a>, <a class="ref" href="symsp_1.html#T2" target="_self" onmouseover="rs('symsp_1/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E4:41_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="c8">p</font>,<font color="Maroon" title="c9">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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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">q</font>,<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c6">a</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="symsp_1.html#T27" target="_self" onmouseover="rs('symsp_1/T27')" onmouseout="rh()">Th27</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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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">q</font>,<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c7">b</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41_3"><span class="lab"><font color="Green" title="E42">A23</font></span></a>, <a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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">q</font>,<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c7">b</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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">q</font>,<font color="Maroon" title="c8">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="c9">q</font>,<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c7">b</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T10" onmouseover="rs('vectsp_1/T10')" onmouseout="rh()">VECTSP_1:10</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">q</font>,<font color="Maroon" title="c8">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="c9">q</font>,<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c7">b</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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">q</font>,<font color="Maroon" title="c7">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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</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">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E1:41_3"><span class="lab"><font color="Green" title="E41">A22</font></span></a>, <a class="ref" href="symsp_1.html#T24" target="_self" onmouseover="rs('symsp_1/T24')" onmouseout="rh()">Th24</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">q</font>,<font color="Maroon" title="c7">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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c7">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="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c6">a</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</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">q</font>,<font color="Maroon" title="c7">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E3:41_3"><span class="lab"><font color="Green" title="E43">A24</font></span></a>, <a class="ref" href="symsp_1.html#T24" target="_self" onmouseover="rs('symsp_1/T24')" onmouseout="rh()">Th24</a></span>
;<br/><span class="kw">hence </span><a NAME="E6:41_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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E8:41"/>
<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="c8">p</font>,<font color="Maroon" title="c9">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="c7">b</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c8">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="c8">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">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="c9">q</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:41"><span class="lab"><font color="Green" title="E40">A16</font></span></a>, <a class="txt" href="#E5:41"><span class="lab"><font color="Green" title="E39">A5</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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