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<b>let </b><font color="Maroon" title="c7">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c8">w</font>, <font color="Maroon" title="c9">y</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c7">V</font>;<br/>





<b>assume </b><a NAME="E1:57"/><i><font color="Green" title="E47">A1</font></i>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c10">POS</font> =  <a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font>;<br/>
<a NAME="E2:57"/><i><font color="Green" title="E48">A2</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font>, <font color="Olive" title="b7">r</font>, <font color="Olive" title="b8">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="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span> holds <br/> ( ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> implies <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b3">c</font> &amp; ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> implies ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> ) ) &amp; ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">r</font>,<font color="Olive" title="b8">s</font> &amp; not <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b7">r</font>,<font color="Olive" title="b8">s</font> implies <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) &amp; ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b7">r</font>,<font color="Olive" title="b8">s</font> &amp; not <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">r</font>,<font color="Olive" title="b8">s</font> implies <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:57"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="analmetr.html#T33" target="_self" title="ANALMETR:th.33">Th33</a>, <a class="ref" href="analmetr.html#T34" target="_self" title="ANALMETR:th.34">Th34</a>, <a class="ref" href="analmetr.html#T35" target="_self" title="ANALMETR:th.35">Th35</a>, <a class="ref" href="analmetr.html#T36" target="_self" title="ANALMETR:th.36">Th36</a>, <a class="ref" href="analmetr.html#T38" target="_self" title="ANALMETR:th.38">Th38</a>, <a class="ref" href="analmetr.html#T40" target="_self" title="ANALMETR:th.40">Th40</a></i>;<br/>
<a NAME="E3:57"/><i><font color="Green" title="E49">A3</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</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="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span>  ex <font color="Olive" title="b4">x</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="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">x</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">x</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:57"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="analmetr.html#T37" target="_self" title="ANALMETR:th.37">Th37</a></i>;<br/>
<b>set </b><font color="Maroon" title="c11">X</font> =  <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 <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span>,the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span> #);<br/>
<a NAME="E4:57"/>
 <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 <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span>,the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span>
 
;<br/>
<a NAME="E5:57"/><b>then </b><i><font color="Green" title="E50">A4</font></i>: 
 <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 <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span>,the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <span class="p1">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c7">V</font></span>)</span>
 
<b>by </b><i><a class="ref" href="analmetr.html#T30" target="_self" title="ANALMETR:th.30">Th30</a></i>;<br/>
<a NAME="E6:57"/>
( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">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="b1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c8">w</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c7">V</font> holds <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) ) &amp; ( for <font color="Olive" title="b1">w1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c7">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 <font color="Olive" title="b1">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c8">w</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c9">y</font></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:57"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="analmetr.html#D1" target="_self" title="ANALMETR:def.1">Def1</a></i>;<br/>
<a NAME="E7:57"/><b>then </b>
 <a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c7">V</font> is   <a href="analoaf.html#NM2" title="ANALOAF:NM.2">OAffinPlane</a>
 
<b>by </b><i><a class="ref" href="analoaf.html#T51" title="ANALOAF:th.51">ANALOAF:51</a></i>;<br/>
<a NAME="E8:57"/><b>then </b>
 <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 <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span>,the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font></span>)</span> #) is   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>
 
<b>by </b><i><a class="txt" href="analmetr.html#E5:57"><i><font color="Green" title="E50">A4</font></i></a>, <a class="ref" href="diraf.html#T53" title="DIRAF:th.53">DIRAF:53</a></i>;<br/>
<b>hence </b><a NAME="E9:57"/>
 <a href="analmetr.html#K2" title="ANALMETR:func.2">AMSpace</a> <font color="Maroon" title="c7">V</font>,<font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">y</font> is   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>
 <b>by </b><i><a class="txt" href="analmetr.html#E2:57"><i><font color="Green" title="E48">A2</font></i></a>, <a class="txt" href="analmetr.html#E3:57"><i><font color="Green" title="E49">A3</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self" title="ANALMETR:def.10">Def10</a></i>;<br/>


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