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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="ortsp_1.html#NM1" title="ORTSP_1:NM.1">OrtSp</a> of <font color="Maroon" title="c4">F</font><br/> for <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font><br/> for <font color="Olive" title="b5">l</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">F</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="b5">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> holds <br/> <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b3">a</font></span>)</span>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">x</font></span><br/><b>let </b><font color="Maroon" title="c5">S</font> be   <a href="ortsp_1.html#NM1" title="ORTSP_1:NM.1">OrtSp</a> of <font color="Maroon" title="c4">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><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">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font><br/> for <font color="Olive" title="b4">l</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">F</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="b4">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> holds <br/> <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b2">a</font></span>)</span>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b3">x</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">x</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"> for <font color="Olive" title="b1">l</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">F</font>  st not <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; <font color="Olive" title="b1">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> holds <br/> <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span><br/><b>let </b><font color="Maroon" title="c9">l</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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"> ( 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="c9">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> implies  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font> )</span><br/>











<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E21">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="c9">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span><br/>

<a NAME="E2:23"/><b>then </b>
not <font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 
<b>by </b><i><a class="ref" href="ortsp_1.html#T15" target="_self" title="ORTSP_1:th.15">Th15</a></i>;<br/>
<a NAME="E3:23"/><b>then </b><i><font color="Green" title="E22">A2</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="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  )
 
<b>by </b><i><a class="txt" href="ortsp_1.html#E1:23"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="ortsp_1.html#T24" target="_self" title="ORTSP_1:th.24">Th24</a></i>;<br/>
<a NAME="E4:23"/><b>then </b>
<font color="Maroon" title="c8">x</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="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</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="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></i>;<br/>
<a NAME="E5:23"/><b>then </b>
<font color="Maroon" title="c8">x</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="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</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="ortsp_1.html#D2" target="_self" title="ORTSP_1:def.2">Def2</a></i>;<br/>
<a NAME="E6:23"/><b>then </b>
<font color="Maroon" title="c8">x</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="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</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="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>;<br/>
<a NAME="E7:23"/><b>then </b>
<font color="Maroon" title="c8">x</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="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</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="ortsp_1.html#E1:23"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></i>;<br/>
<a NAME="E8:23"/><b>then </b>
<font color="Maroon" title="c8">x</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="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</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="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>;<br/>
<a NAME="E9:23"/><b>then </b>
<font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 
<b>by </b><i><a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></i>;<br/>
<b>hence </b><a NAME="E10:23"/>
 <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:23"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="ortsp_1.html#E3:23"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="ortsp_1.html#T20" target="_self" title="ORTSP_1:th.20">Th20</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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