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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</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">w</font>, <font color="Olive" title="b2">y</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font>, <font color="Olive" title="b5">r</font>, <font color="Olive" title="b6">r1</font>, <font color="Olive" title="b7">r2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font>)</span>)</span>  st  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">r</font>,<font color="Olive" title="b6">r1</font> &amp; <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">r</font>,<font color="Olive" title="b7">r2</font> holds <br/><font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b6">r1</font>,<font color="Olive" title="b7">r2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">w</font>, <font color="Maroon" title="c3">y</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</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">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font>, <font color="Olive" title="b4">r1</font>, <font color="Olive" title="b5">r2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>)</span>)</span>  st  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">r</font>,<font color="Olive" title="b4">r1</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">r</font>,<font color="Olive" title="b5">r2</font> holds <br/><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b4">r1</font>,<font color="Olive" title="b5">r2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</font>, <font color="Maroon" title="c6">r</font>, <font color="Maroon" title="c7">r1</font>, <font color="Maroon" title="c8">r2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</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"> (  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">r</font>,<font color="Maroon" title="c7">r1</font> &amp; <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">r</font>,<font color="Maroon" title="c8">r2</font> implies <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c7">r1</font>,<font color="Maroon" title="c8">r2</font> )</span><br/>















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:44"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 <span class="kw">and </span><br/><a NAME="E2:44"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">r</font>,<font color="Maroon" title="c7">r1</font>
 <span class="kw">and </span><br/><a NAME="E3:44"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">r</font>,<font color="Maroon" title="c8">r2</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="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c7">r1</font>,<font color="Maroon" title="c8">r2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c9">u</font> = <font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c10">v</font> = <font color="Maroon" title="c5">q</font>, <font color="Maroon" title="c11">w1</font> = <font color="Maroon" title="c6">r</font>, <font color="Maroon" title="c12">v1</font> = <font color="Maroon" title="c7">r1</font>, <font color="Maroon" title="c13">v2</font> = <font color="Maroon" title="c8">r2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<a NAME="E5:44"/>
<font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">w1</font>,<font color="Maroon" title="c13">v2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="analmetr.html#T21" target="_self" onmouseover="rs('analmetr/T21')" onmouseout="rh()">Th21</a></span>;<br/>
<a NAME="E6:44"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A4</font></span>: 
<font color="Maroon" title="c10">v</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c13">v2</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c11">w1</font> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 
;<br/>
<span class="lab"><font color="Green" title="E38">A5</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c13">v2</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c11">w1</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c11">w1</font></span>)</span> = 
<font color="Maroon" title="c13">v2</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"><font color="Maroon" title="c12">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c11">w1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c11">w1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T27" onmouseover="rs('rlvect_1/T27')" onmouseout="rh()">RLVECT_1:27</a></span>
<br/>.= 
<font color="Maroon" title="c13">v2</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">w1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c11">w1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T29" onmouseover="rs('rlvect_1/T29')" onmouseout="rh()">RLVECT_1:29</a></span>
<br/>.= 
<font color="Maroon" title="c13">v2</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T15" onmouseover="rs('rlvect_1/T15')" onmouseout="rh()">RLVECT_1:15</a></span>
<br/>.= 
<font color="Maroon" title="c13">v2</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c12">v1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T13" onmouseover="rs('rlvect_1/T13')" onmouseout="rh()">RLVECT_1:13</a></span>
;<br/>
<a NAME="E8:44"/>
<font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">w1</font>,<font color="Maroon" title="c12">v1</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="analmetr.html#T21" target="_self" onmouseover="rs('analmetr/T21')" onmouseout="rh()">Th21</a></span>;<br/>
<a NAME="E9:44"/><span class="kw">then </span>
<font color="Maroon" title="c10">v</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c12">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c11">w1</font> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 
;<br/>
<a NAME="E10:44"/><span class="kw">then </span>
<font color="Maroon" title="c10">v</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c9">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c13">v2</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c11">w1</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c11">w1</font></span>)</span> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E6:44"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="analmetr.html#T10" target="_self" onmouseover="rs('analmetr/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<a NAME="E11:44"/><span class="kw">then </span>
<font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c12">v1</font>,<font color="Maroon" title="c13">v2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:44"><span class="lab"><font color="Green" title="E38">A5</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:44"/>
<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c7">r1</font>,<font color="Maroon" title="c8">r2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T21" target="_self" onmouseover="rs('analmetr/T21')" onmouseout="rh()">Th21</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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