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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of  <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</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">v</font>, <font color="Olive" title="b2">w</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">w1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="dualsp01.html#K4" title="DUALSP01:func.4">RVSp2RLSp</a> <font color="Maroon" title="c1">X</font></span>)</span>  st <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v1</font> &amp; <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">w1</font> holds <br/>( <font color="Olive" title="b1">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">w1</font> &amp; <font color="Olive" title="b1">v</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">w1</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">v</font>, <font color="Maroon" title="c3">w</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</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">v1</font>, <font color="Olive" title="b2">w1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="dualsp01.html#K4" title="DUALSP01:func.4">RVSp2RLSp</a> <font color="Maroon" title="c1">X</font></span>)</span>  st <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v1</font> &amp; <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">w1</font> holds <br/>( <font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">w1</font> &amp; <font color="Maroon" title="c2">v</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">w1</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">v1</font>, <font color="Maroon" title="c5">w1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="dualsp01.html#K4" title="DUALSP01:func.4">RVSp2RLSp</a> <font color="Maroon" title="c1">X</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"> ( <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> &amp; <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">w1</font> implies ( <font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">w1</font> &amp; <font color="Maroon" title="c2">v</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c5">w1</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:8"/><span class="lab"><font color="Green" title="E3">AS</font></span>: 
( <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> &amp; <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">w1</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"> ( <font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">w1</font> &amp; <font color="Maroon" title="c2">v</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c5">w1</font> )</span><br/>

 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">w1</font> = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">w1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T16" onmouseover="rs('rlvect_1/T16')" onmouseout="rh()">RLVECT_1:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c3">w</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8"><span class="lab"><font color="Green" title="E3">AS</font></span></a></span>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">w</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T14" onmouseover="rs('vectsp_1/T14')" onmouseout="rh()">VECTSP_1:14</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:8"/>
( <font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">w1</font> &amp; <font color="Maroon" title="c2">v</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c5">w1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8"><span class="lab"><font color="Green" title="E3">AS</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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