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<b>let </b><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being  <a href="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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>











<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E27">A1</font></i>: 
( 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>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="E2:33"/><b>then </b>
not <font color="Maroon" title="c6">b</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 
<b>by </b><i><a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/>
<a NAME="E3:33"/><b>then </b>
not <font color="Maroon" title="c6">b</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 
<b>by </b><i><a class="txt" href="symsp_1.html#E1:33"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="symsp_1.html#T14" target="_self" title="SYMSP_1:th.14">Th14</a></i>;<br/>
<a NAME="E4:33"/><b>then </b><i><font color="Green" title="E28">A2</font></i>: 
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> 
 
<b>by </b><i><a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/>
<a NAME="E5:33"/><b>then </b><i><font color="Green" title="E29">A3</font></i>: 
( <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <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>  )
 
<b>by </b><i><a class="txt" href="symsp_1.html#E1:33"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="symsp_1.html#T27" target="_self" title="SYMSP_1:th.27">Th27</a></i>;<br/>
<a NAME="E6:33"/>
( <font color="Maroon" title="c8">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Maroon" title="c8">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  )
 
<b>by </b><i><a class="txt" href="symsp_1.html#E1:33"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/>
<a NAME="E7:33"/><b>then </b>
( <font color="Maroon" title="c8">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Maroon" title="c8">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  )
 
<b>by </b><i><a class="ref" href="symsp_1.html#D1" target="_self" title="SYMSP_1:def.1">Def1</a></i>;<br/>
<a NAME="E8:33"/><b>then </b>
( <font color="Maroon" title="c8">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Maroon" title="c8">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  )
 
<b>by </b><i><a class="ref" href="symsp_1.html#T16" target="_self" title="SYMSP_1:th.16">Th16</a></i>;<br/>
<a NAME="E9:33"/><b>then </b>
<font color="Maroon" title="c8">p</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 
<b>by </b><i><a class="ref" href="symsp_1.html#D1" target="_self" title="SYMSP_1:def.1">Def1</a></i>;<br/>
<a NAME="E10:33"/><b>then </b><i><font color="Green" title="E30">A4</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</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> 
 
<b>by </b><i><a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/>
<a NAME="E11:33"/>
<font color="Maroon" title="c9">c</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</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> 
 
<b>by </b><i><a class="txt" href="symsp_1.html#E5:33"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/>
<a NAME="E12:33"/><b>then </b>
<font color="Maroon" title="c9">c</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</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> 
 
<b>by </b><i><a class="txt" href="symsp_1.html#E10:33"><i><font color="Green" title="E30">A4</font></i></a>, <a class="ref" href="symsp_1.html#D1" target="_self" title="SYMSP_1:def.1">Def1</a></i>;<br/>
<a NAME="E13:33"/><b>then </b>
<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> 
 
<b>by </b><i><a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/>
<b>hence </b><a NAME="E14:33"/>
 <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>
 <b>by </b><i><a class="txt" href="symsp_1.html#E4:33"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="symsp_1.html#E5:33"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="symsp_1.html#T24" target="_self" title="SYMSP_1:th.24">Th24</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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