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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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">u1</font>, <font color="Olive" title="b5">v</font>, <font color="Olive" title="b6">v1</font>, <font color="Olive" title="b7">w</font>, <font color="Olive" title="b8">w1</font>, <font color="Olive" title="b9">u2</font>, <font color="Olive" title="b10">v2</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  st  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u1</font>,<font color="Olive" title="b5">v</font>,<font color="Olive" title="b6">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b5">v</font>,<font color="Olive" title="b6">v1</font>,<font color="Olive" title="b7">w</font>,<font color="Olive" title="b8">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u1</font>,<font color="Olive" title="b9">u2</font>,<font color="Olive" title="b10">v2</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp;  not <font color="Olive" title="b9">u2</font>,<font color="Olive" title="b10">v2</font>,<font color="Olive" title="b7">w</font>,<font color="Olive" title="b8">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp;  not <font color="Olive" title="b5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">v1</font> holds <br/><font color="Olive" title="b3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">u1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">u1</font>, <font color="Maroon" title="c6">v</font>, <font color="Maroon" title="c7">v1</font>, <font color="Maroon" title="c8">w</font>, <font color="Maroon" title="c9">w1</font>, <font color="Maroon" title="c10">u2</font>, <font color="Maroon" title="c11">v2</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" 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">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp;  not <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp;  not <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> implies <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u1</font> )</span><br/>





















<span class="kw">assume </span><a NAME="E1:57"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</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="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> or  not <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> or  not <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> or <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> or <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> or <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u1</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:57"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <span class="kw">and </span><br/><a NAME="E3:57"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <span class="kw">and </span><br/><a NAME="E4:57"/><span class="lab"><font color="Green" title="E35">A4</font></span>: 
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> or <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> or <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u1</font> )</span><br/>

<a NAME="E5:57"/><span class="lab"><font color="Green" title="E36">A5</font></span>: 
 <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>), <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">u1</font>) <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></span>;<br/>
<a NAME="E6:57"/><span class="lab"><font color="Green" title="E37">A6</font></span>: 
 <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">v</font>), <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c7">v1</font>) <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></span>;<br/>
<a NAME="E7:57"/><span class="lab"><font color="Green" title="E38">A7</font></span>: 
 <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>), <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">u1</font>) <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:57_1"/><span class="lab"><font color="Green" title="E39">A8</font></span>: 
<font color="Maroon" title="c4">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">u1</font>
 <span class="kw">and </span><br/><a NAME="E2:57_1"/><span class="lab"><font color="Green" title="E40">A9</font></span>: 
<font color="Maroon" title="c6">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">v1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> or <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> or <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u1</font> )</span><br/><a NAME="E3:57_1"/>
<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E5:57"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="txt" href="#E7:57"><span class="lab"><font color="Green" title="E38">A7</font></span></a>, <a class="txt" href="#E1:57_1"><span class="lab"><font color="Green" title="E39">A8</font></span></a>, <a class="ref" href="analort.html#T6" target="_self" title="ANALORT:th.6">Th6</a>, <a class="ref" href="analoaf.html#T11" title="ANALOAF:th.11">ANALOAF:11</a></span>;<br/><a NAME="E4:57_1"/><span class="kw">then </span>
 <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">v</font>), <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c7">v1</font>) <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c10">u2</font>), <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c11">v2</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="analort.html#T17" target="_self" title="ANALORT:th.17">Th17</a></span>;<br/><a NAME="E5:57_1"/><span class="kw">then </span>
 <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c10">u2</font>), <a href="analort.html#K1" title="ANALORT:func.1">Ortm</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c11">v2</font>) <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E6:57"><span class="lab"><font color="Green" title="E37">A6</font></span></a>, <a class="txt" href="#E2:57_1"><span class="lab"><font color="Green" title="E40">A9</font></span></a>, <a class="ref" href="analort.html#T6" target="_self" title="ANALORT:th.6">Th6</a>, <a class="ref" href="analoaf.html#T11" title="ANALOAF:th.11">ANALOAF:11</a></span>;<br/><span class="kw">hence </span><a NAME="E6:57_1"/>
( <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> or <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> or <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E9:57"/>
( <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> or <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> or <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u1</font> )
 ; <a class="txt" 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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