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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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</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>  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> holds <br/>for <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font>, <font color="Olive" title="b5">u1</font>, <font color="Olive" title="b6">v1</font>, <font color="Olive" title="b7">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  st not <font color="Olive" title="b3">v</font>,<font color="Olive" title="b6">v1</font>,<font color="Olive" title="b4">w</font>,<font color="Olive" title="b5">u1</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="b3">v</font>,<font color="Olive" title="b6">v1</font>,<font color="Olive" title="b5">u1</font>,<font color="Olive" title="b4">w</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">u1</font>,<font color="Olive" title="b7">w1</font>,<font color="Olive" title="b5">u1</font>,<font color="Olive" title="b4">w</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> holds <br/> ex <font color="Olive" title="b8">u2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( ( <font color="Olive" title="b3">v</font>,<font color="Olive" title="b6">v1</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b8">u2</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> or <font color="Olive" title="b3">v</font>,<font color="Olive" title="b6">v1</font>,<font color="Olive" title="b8">u2</font>,<font color="Olive" title="b3">v</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">u1</font>,<font color="Olive" title="b7">w1</font>,<font color="Olive" title="b5">u1</font>,<font color="Olive" title="b8">u2</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> or <font color="Olive" title="b5">u1</font>,<font color="Olive" title="b7">w1</font>,<font color="Olive" title="b8">u2</font>,<font color="Olive" title="b5">u1</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> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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> implies for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font>, <font color="Olive" title="b3">u1</font>, <font color="Olive" title="b4">v1</font>, <font color="Olive" title="b5">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  st not <font color="Olive" title="b1">v</font>,<font color="Olive" title="b4">v1</font>,<font color="Olive" title="b2">w</font>,<font color="Olive" title="b3">u1</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="Olive" title="b1">v</font>,<font color="Olive" title="b4">v1</font>,<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b2">w</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="Olive" title="b3">u1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b2">w</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> holds <br/> ex <font color="Olive" title="b6">u2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( ( <font color="Olive" title="b1">v</font>,<font color="Olive" title="b4">v1</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b6">u2</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="Olive" title="b1">v</font>,<font color="Olive" title="b4">v1</font>,<font color="Olive" title="b6">u2</font>,<font color="Olive" title="b1">v</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="Olive" title="b3">u1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b6">u2</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="Olive" title="b3">u1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b6">u2</font>,<font color="Olive" title="b3">u1</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><br/>





<span class="kw">assume </span><a NAME="E1:63"/><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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font>, <font color="Olive" title="b3">u1</font>, <font color="Olive" title="b4">v1</font>, <font color="Olive" title="b5">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  st not <font color="Olive" title="b1">v</font>,<font color="Olive" title="b4">v1</font>,<font color="Olive" title="b2">w</font>,<font color="Olive" title="b3">u1</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="Olive" title="b1">v</font>,<font color="Olive" title="b4">v1</font>,<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b2">w</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="Olive" title="b3">u1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b2">w</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> holds <br/> ex <font color="Olive" title="b6">u2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( ( <font color="Olive" title="b1">v</font>,<font color="Olive" title="b4">v1</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b6">u2</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="Olive" title="b1">v</font>,<font color="Olive" title="b4">v1</font>,<font color="Olive" title="b6">u2</font>,<font color="Olive" title="b1">v</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="Olive" title="b3">u1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b6">u2</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="Olive" title="b3">u1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b6">u2</font>,<font color="Olive" title="b3">u1</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><br/>

<span class="kw">let </span><font color="Maroon" title="c4">v</font>, <font color="Maroon" title="c5">w</font>, <font color="Maroon" title="c6">u1</font>, <font color="Maroon" title="c7">v1</font>, <font color="Maroon" title="c8">w1</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="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u1</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="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">w</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">u1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">w</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> implies  ex <font color="Olive" title="b1">u2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( ( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">v</font>,<font color="Olive" title="b1">u2</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="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Olive" title="b1">u2</font>,<font color="Maroon" title="c4">v</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">u1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">u2</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">u1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Olive" title="b1">u2</font>,<font color="Maroon" title="c6">u1</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><br/>









<span class="kw">consider </span><font color="Maroon" title="c9">u</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E3:63"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">u</font>
 <span class="kw">and </span><br/><a NAME="E4:63"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c9">u</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">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="analort.html#T41" target="_self" title="ANALORT:th.41">Th41</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E5:63"/><span class="lab"><font color="Green" title="E35">A4</font></span>: 
not <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u1</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="E6:63"/><span class="lab"><font color="Green" title="E36">A5</font></span>: 
not <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">w</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="E7:63"/><span class="lab"><font color="Green" title="E37">A6</font></span>: 
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">w</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="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">u2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( ( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">v</font>,<font color="Olive" title="b1">u2</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="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Olive" title="b1">u2</font>,<font color="Maroon" title="c4">v</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">u1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">u2</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">u1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Olive" title="b1">u2</font>,<font color="Maroon" title="c6">u1</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><br/>

<a NAME="E8:63"/><span class="lab"><font color="Green" title="E38">A7</font></span>: 
not  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font>, <a href="analort.html#K2" title="ANALORT:func.2">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="c5">w</font>,<font color="Maroon" title="c6">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63"><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/>
<a NAME="E9:63"/><span class="lab"><font color="Green" title="E39">A8</font></span>: 
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font>, <a href="analort.html#K2" title="ANALORT:func.2">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="c4">v</font>,<font color="Maroon" title="c9">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63"><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="E10:63"/><span class="lab"><font color="Green" title="E40">A9</font></span>: 
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">u1</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">w1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:63"><span class="lab"><font color="Green" title="E37">A6</font></span></a>, <a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></span>;<br/>
<a NAME="E11:63"/><span class="lab"><font color="Green" title="E41">A10</font></span>: 
not  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font>, <a href="analort.html#K2" title="ANALORT:func.2">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="c6">u1</font>,<font color="Maroon" title="c5">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:63"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></span>;<br/>
<a NAME="E12:63"/><span class="lab"><font color="Green" title="E42">A11</font></span>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c9">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c7">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:63"><span class="lab"><font color="Green" title="E39">A8</font></span></a>, <a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></span>;<br/>
<a NAME="E13:63"/><span class="lab"><font color="Green" title="E43">A12</font></span>: 
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">w</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">u1</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">w1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:63"><span class="lab"><font color="Green" title="E40">A9</font></span></a>, <a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></span>;<br/>
<a NAME="E14:63"/><span class="lab"><font color="Green" title="E44">A13</font></span>: 
<font color="Maroon" title="c6">u1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:63"><span class="lab"><font color="Green" title="E38">A7</font></span></a>, <a class="ref" href="analoaf.html#T18" title="ANALOAF:th.18">ANALOAF:18</a></span>;<br/>
<a NAME="E15:63"/><span class="lab"><font color="Green" title="E45">A14</font></span>: 
not <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c9">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="txt" href="#E11:63"><span class="lab"><font color="Green" title="E41">A10</font></span></a>, <a class="txt" href="#E12:63"><span class="lab"><font color="Green" title="E42">A11</font></span></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</a></span>;<br/>
<a NAME="E16:63"/><span class="lab"><font color="Green" title="E46">A15</font></span>: 
not <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c9">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c6">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="txt" href="#E8:63"><span class="lab"><font color="Green" title="E38">A7</font></span></a>, <a class="txt" href="#E12:63"><span class="lab"><font color="Green" title="E42">A11</font></span></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</a></span>;<br/>
<a NAME="E17:63"/>
(  <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> implies  ex <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>for <font color="Olive" title="b3">w</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  ex <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <span class="p1">(<span class="default"><font color="Olive" title="b4">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b1">u</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">w</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:63_1"/><span class="lab"><font color="Green" title="E47">A16</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="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>for <font color="Olive" title="b3">w</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  ex <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <span class="p1">(<span class="default"><font color="Olive" title="b4">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b1">u</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">w</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c2">x</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">v</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>for <font color="Olive" title="b2">w</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  ex <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b1">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">w</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c3">y</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">w</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  ex <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">w</font></span><br/>

<span class="kw">thus </span><a NAME="E2:63_1"/>
for <font color="Olive" title="b1">w</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  ex <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="analort.html#K1" title="ANALORT:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1"><span class="lab"><font color="Green" title="E47">A16</font></span></a>, <a class="ref" href="analmetr.html#D1" title="ANALMETR:def.1">ANALMETR:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">u2</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E19:63"/><span class="lab"><font color="Green" title="E47">A17</font></span>: 
( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c9">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c10">u2</font> or <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c9">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c4">v</font> )
 <span class="kw">and </span><br/><a NAME="E20:63"/><span class="lab"><font color="Green" title="E48">A18</font></span>: 
( <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">w</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c10">u2</font> or <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c5">w</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c6">u1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E15:63"><span class="lab"><font color="Green" title="E45">A14</font></span></a>, <a class="txt" href="#E16:63"><span class="lab"><font color="Green" title="E46">A15</font></span></a>, <a class="ref" href="analoaf.html#T31" title="ANALOAF:th.31">ANALOAF:31</a></span>;<br/>
<a NAME="E21:63"/>
(  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font>, <a href="analort.html#K2" title="ANALORT:func.2">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="c4">v</font>,<font color="Maroon" title="c10">u2</font> or  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font>, <a href="analort.html#K2" title="ANALORT:func.2">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="c10">u2</font>,<font color="Maroon" title="c4">v</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="txt" href="#E12:63"><span class="lab"><font color="Green" title="E42">A11</font></span></a>, <a class="txt" href="#E19:63"><span class="lab"><font color="Green" title="E47">A17</font></span></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</a></span>;<br/>
<a NAME="E22:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A19</font></span>: 
( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c10">u2</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="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c4">v</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">by</span> <span class="lab"><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></span>;<br/>
<a NAME="E23:63"/>
(  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">u1</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">w1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c10">u2</font> or  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c6">u1</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">w1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c6">u1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:63"><span class="lab"><font color="Green" title="E43">A12</font></span></a>, <a class="txt" href="#E14:63"><span class="lab"><font color="Green" title="E44">A13</font></span></a>, <a class="txt" href="#E20:63"><span class="lab"><font color="Green" title="E48">A18</font></span></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</a></span>;<br/>
<a NAME="E24:63"/><span class="kw">then </span>
( <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c10">u2</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">u1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c6">u1</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">by</span> <span class="lab"><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E25:63"/>
 ex <font color="Olive" title="b1">u2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( ( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">v</font>,<font color="Olive" title="b1">u2</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="c4">v</font>,<font color="Maroon" title="c7">v1</font>,<font color="Olive" title="b1">u2</font>,<font color="Maroon" title="c4">v</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">u1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">u2</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">u1</font>,<font color="Maroon" title="c8">w1</font>,<font color="Olive" title="b1">u2</font>,<font color="Maroon" title="c6">u1</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">by</span> <span class="lab"><a class="txt" href="#E22:63"><span class="lab"><font color="Green" title="E49">A19</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
