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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">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">u1</font>, <font color="Olive" title="b4">v1</font>, <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">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="b7">p</font>, <font color="Olive" title="b8">q</font>, <font color="Olive" title="b9">r</font>, <font color="Olive" title="b10">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analort.html#K6" title="ANALORT:func.6">CESpace</a> <font color="Maroon" title="c1">V</font>,<font color="Olive" title="b5">x</font>,<font color="Olive" title="b6">y</font></span>)</span>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">p</font> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">q</font> &amp; <font color="Olive" title="b3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b9">r</font> &amp; <font color="Olive" title="b4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b10">s</font> holds <br/>( <font color="Olive" title="b7">p</font>,<font color="Olive" title="b8">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">r</font>,<font color="Olive" title="b10">s</font> iff <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Olive" title="b5">x</font>,<font color="Olive" title="b6">y</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">u1</font>, <font color="Maroon" title="c5">v1</font>, <font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">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"> 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">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analort.html#K6" title="ANALORT:func.6">CESpace</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span>)</span>  st <font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> &amp; <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> &amp; <font color="Maroon" title="c4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">r</font> &amp; <font color="Maroon" title="c5">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">s</font> holds <br/>( <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">r</font>,<font color="Olive" title="b4">s</font> iff <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">p</font>, <font color="Maroon" title="c9">q</font>, <font color="Maroon" title="c10">r</font>, <font color="Maroon" title="c11">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analort.html#K6" title="ANALORT:func.6">CESpace</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">p</font> &amp; <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q</font> &amp; <font color="Maroon" title="c4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">r</font> &amp; <font color="Maroon" title="c5">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">s</font> implies ( <font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> iff <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> ) )</span><br/>





















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:71"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">p</font>
 <span class="kw">and </span><br/><a NAME="E2:71"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q</font>
 <span class="kw">and </span><br/><a NAME="E3:71"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
<font color="Maroon" title="c4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">r</font>
 <span class="kw">and </span><br/><a NAME="E4:71"/><span class="lab"><font color="Green" title="E37">A4</font></span>: 
<font color="Maroon" title="c5">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> iff <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> )</span><br/>

<a NAME="E5:71"/><span class="lab"><font color="Green" title="E38">A5</font></span>: 
( <font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> implies <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:71_1"/>
<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span><br/>

<a NAME="E2:71_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analort.html#K6" title="ANALORT:func.6">CESpace</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">u19</font>, <font color="Maroon" title="c13">u29</font>, <font color="Maroon" title="c14">v19</font>, <font color="Maroon" title="c15">v29</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="E4:71_1"/><span class="lab"><font color="Green" title="E39">A6</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">u19</font>,<font color="Maroon" title="c13">u29</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E5:71_1"/><span class="lab"><font color="Green" title="E40">A7</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">v19</font>,<font color="Maroon" title="c15">v29</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E6:71_1"/><span class="lab"><font color="Green" title="E41">A8</font></span>: 
<font color="Maroon" title="c12">u19</font>,<font color="Maroon" title="c13">u29</font>,<font color="Maroon" title="c14">v19</font>,<font color="Maroon" title="c15">v29</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E3:71"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="txt" href="#E4:71"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="analort.html#D5" target="_self" title="ANALORT:def.5">Def5</a></span>;<br/>
<a NAME="E7:71_1"/><span class="lab"><font color="Green" title="E42">A9</font></span>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">u19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:71_1"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<a NAME="E8:71_1"/><span class="lab"><font color="Green" title="E43">A10</font></span>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">u29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:71_1"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<a NAME="E9:71_1"/>
<font color="Maroon" title="c4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">v19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_1"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:71_1"/>
<font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_1"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="txt" href="#E6:71_1"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="txt" href="#E7:71_1"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="txt" href="#E8:71_1"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</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>
<a NAME="E6:71"/>
( <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> implies <font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:71_2"/>
<font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font></span><br/>

<a NAME="E2:71_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><a href="analort.html#K4" title="ANALORT:func.4">CORTE</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analort.html#D5" target="_self" title="ANALORT:def.5">Def5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:71_2"/>
<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E3:71"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="txt" href="#E4:71"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</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">hence </span><a NAME="E7:71"/>
( <font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">r</font>,<font color="Maroon" title="c11">s</font> iff <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="analort.html#R1" title="ANALORT:pred.1">are_COrte_wrt</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71"><span class="lab"><font color="Green" title="E38">A5</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/>


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