<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="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">b</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font>  st  not <font color="Olive" title="b3">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Olive" title="b2">b</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Olive" title="b5">c</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  holds <br/> <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">p</font></span>)</span>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b5">c</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="Olive" title="b3">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b5">c</font>)</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>  st  not <font color="Olive" title="b2">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Olive" title="b1">b</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Olive" title="b4">c</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  holds <br/> <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">p</font></span>)</span>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b4">c</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="Olive" title="b2">a</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b4">c</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">p</font>, <font color="Maroon" title="c9">c</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="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Maroon" title="c6">b</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Maroon" title="c9">c</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  implies  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c8">p</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">c</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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">c</font>) )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:33"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
 not <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">and </span><br/><a NAME="E2:33"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c6">b</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">and </span><br/><a NAME="E3:33"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<font color="Maroon" title="c9">c</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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c8">p</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">c</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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">c</font>)</span><br/>

<a NAME="E4:33"/>
<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="#E2:33"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="symsp_1.html#T2" target="_self" title="SYMSP_1:th.2">Th12</a></span>;<br/>
<a NAME="E5:33"/><span class="kw">then </span>
<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="ref" href="symsp_1.html#D1" target="_self" title="SYMSP_1:def.1">Def1</a></span>;<br/>
<a NAME="E6:33"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A4</font></span>: 
<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="ref" href="symsp_1.html#T6" target="_self" title="SYMSP_1:th.6">Th16</a></span>;<br/>
<a NAME="E7:33"/>
<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="#E3:33"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="symsp_1.html#T2" target="_self" title="SYMSP_1:th.2">Th12</a></span>;<br/>
<a NAME="E8:33"/><span class="kw">then </span>
<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="#E6:33"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="symsp_1.html#D1" target="_self" title="SYMSP_1:def.1">Def1</a></span>;<br/>
<a NAME="E9:33"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A5</font></span>: 
<font color="Maroon" title="c9">c</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">c</font>)</span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c6">b</font></span>)</span> <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" title="SYMSP_1:th.2">Th12</a></span>;<br/>
<a NAME="E10:33"/>
<font color="Maroon" title="c7">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="#E1:33"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="symsp_1.html#T14" target="_self" title="SYMSP_1:th.14">Th27</a></span>;<br/>
<a NAME="E11:33"/><span class="kw">then </span>
<font color="Maroon" title="c9">c</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">c</font>)</span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c6">b</font></span>)</span> <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" title="SYMSP_1:th.2">Th12</a></span>;<br/>
<a NAME="E12:33"/><span class="kw">then </span>
<font color="Maroon" title="c9">c</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">c</font>)</span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:33"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="ref" href="symsp_1.html#D1" target="_self" title="SYMSP_1:def.1">Def1</a></span>;<br/>
<a NAME="E13:33"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A6</font></span>: 
<font color="Maroon" title="c7">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <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="ref" href="symsp_1.html#T2" target="_self" title="SYMSP_1:th.2">Th12</a></span>;<br/>
<a NAME="E14:33"/>
 not <font color="Maroon" title="c6">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="#E1:33"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="symsp_1.html#T2" target="_self" title="SYMSP_1:th.2">Th12</a></span>;<br/>
<a NAME="E15:33"/><span class="kw">then </span>
 not <font color="Maroon" title="c6">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="#E2:33"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="symsp_1.html#T4" target="_self" title="SYMSP_1:th.4">Th14</a></span>;<br/>
<a NAME="E16:33"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A7</font></span>: 
 not <font color="Maroon" title="c7">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <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="ref" href="symsp_1.html#T2" target="_self" title="SYMSP_1:th.2">Th12</a></span>;<br/>
<a NAME="E17:33"/><span class="kw">then </span>
<font color="Maroon" title="c7">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <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="ref" href="symsp_1.html#T14" target="_self" title="SYMSP_1:th.14">Th27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:33"/>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c8">p</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">c</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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:33"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="txt" href="#E13:33"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
