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<span class="kw">let </span><font color="Maroon" title="c7">POS</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="analmetr.html#L2" title="ANALMETR:struct.2">ParOrtStr</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"> ( <font color="Maroon" title="c7">POS</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">OrtAfPl-like</a>  iff (  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; (  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 <font color="Maroon" title="c7">POS</font> holds <br/> ( <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="b2">b</font>,<font color="Olive" title="b1">a</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="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="analoaf.html#R2" title="ANALOAF:pred.2">//</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="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> ) &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="b1">a</font>,<font color="Olive" title="b3">c</font> implies <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> ) &amp;  not  for <font color="Olive" title="b9">x</font>, <font color="Olive" title="b10">y</font>, <font color="Olive" title="b11">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b9">x</font>,<font color="Olive" title="b10">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">x</font>,<font color="Olive" title="b11">z</font> &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">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="b9">x</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="b2">b</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b9">x</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="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> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> 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="b9">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="b9">x</font> ) &amp; (  not <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="b3">c</font>,<font color="Olive" title="b4">d</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b1">a</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b9">x</font> ) ) ) ) ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">P</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 <font color="Maroon" title="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #);<br/>
<div><span class="kw">hereby </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"> (  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; (  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 <font color="Maroon" title="c7">POS</font> holds <br/> ( <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="b2">b</font>,<font color="Olive" title="b1">a</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="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="analoaf.html#R2" title="ANALOAF:pred.2">//</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="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> ) &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="b1">a</font>,<font color="Olive" title="b3">c</font> implies <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> ) &amp;  not  for <font color="Olive" title="b9">x</font>, <font color="Olive" title="b10">y</font>, <font color="Olive" title="b11">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b9">x</font>,<font color="Olive" title="b10">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">x</font>,<font color="Olive" title="b11">z</font> &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">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="b9">x</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="b2">b</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b9">x</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="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> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> 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="b9">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="b9">x</font> ) &amp; (  not <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="b3">c</font>,<font color="Olive" title="b4">d</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b1">a</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b9">x</font> ) ) ) ) implies <font color="Maroon" title="c7">POS</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">OrtAfPl-like</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:64_1"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
<font color="Maroon" title="c7">POS</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">OrtAfPl-like</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"> (  ex <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> &amp; (  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 <font color="Maroon" title="c7">POS</font> holds <br/> ( <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="b2">b</font>,<font color="Olive" title="b1">a</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="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="analoaf.html#R2" title="ANALOAF:pred.2">//</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="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> ) &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="b1">a</font>,<font color="Olive" title="b3">c</font> implies <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> ) &amp;  not  for <font color="Olive" title="b9">x</font>, <font color="Olive" title="b10">y</font>, <font color="Olive" title="b11">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b9">x</font>,<font color="Olive" title="b10">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">x</font>,<font color="Olive" title="b11">z</font> &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">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="b9">x</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="b2">b</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b9">x</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="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> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> 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="b9">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="b9">x</font> ) &amp; (  not <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="b3">c</font>,<font color="Olive" title="b4">d</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b1">a</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b9">x</font> ) ) ) ) )</span><br/><a NAME="E2:64_1"/><span class="kw">then </span>
 <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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) is   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>
 ;<br/><span class="kw">hence </span><a NAME="E3:64_1"/>
 ex <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T46" onmouseover="rs('diraf/T46')" onmouseout="rh()">DIRAF:46</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">  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 <font color="Maroon" title="c7">POS</font> holds <br/> ( <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="b2">b</font>,<font color="Olive" title="b1">a</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="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="analoaf.html#R2" title="ANALOAF:pred.2">//</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="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> ) &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="b1">a</font>,<font color="Olive" title="b3">c</font> implies <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> ) &amp;  not  for <font color="Olive" title="b9">x</font>, <font color="Olive" title="b10">y</font>, <font color="Olive" title="b11">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b9">x</font>,<font color="Olive" title="b10">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">x</font>,<font color="Olive" title="b11">z</font> &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">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="b9">x</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="b2">b</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b9">x</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="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> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> 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="b9">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="b9">x</font> ) &amp; (  not <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="b3">c</font>,<font color="Olive" title="b4">d</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b1">a</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b9">x</font> ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font>, <font color="Maroon" title="c11">c</font>, <font color="Maroon" title="c12">d</font>, <font color="Maroon" title="c13">p</font>, <font color="Maroon" title="c14">q</font>, <font color="Maroon" title="c15">r</font>, <font color="Maroon" title="c16">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</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="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">c</font> implies <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> ) &amp;  not  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">d</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">x</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; (  not <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> ) ) )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c17">a9</font> = <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c18">b9</font> = <font color="Maroon" title="c10">b</font>, <font color="Maroon" title="c19">c9</font> = <font color="Maroon" title="c11">c</font>, <font color="Maroon" title="c20">d9</font> = <font color="Maroon" title="c12">d</font>, <font color="Maroon" title="c21">p9</font> = <font color="Maroon" title="c13">p</font>, <font color="Maroon" title="c22">q9</font> = <font color="Maroon" title="c14">q</font>, <font color="Maroon" title="c23">r9</font> = <font color="Maroon" title="c15">r</font>, <font color="Maroon" title="c24">s9</font> = <font color="Maroon" title="c16">s</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) ;<br/><span class="kw">consider </span><font color="Maroon" title="c25">x9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #)<span class="kw"> such that </span><br/><a NAME="E6:64_1"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
( <font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c9</font>,<font color="Maroon" title="c25">x9</font> &amp; <font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c19">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c25">x9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="diraf.html#T46" onmouseover="rs('diraf/T46')" onmouseout="rh()">DIRAF:46</a></span>;<br/><a NAME="E7:64_1"/>
( <font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c17">a9</font> &amp; <font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c9</font>,<font color="Maroon" title="c19">c9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="diraf.html#T46" onmouseover="rs('diraf/T46')" onmouseout="rh()">DIRAF:46</a></span>;<br/><span class="kw">hence </span><a NAME="E8:64_1"/>
( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</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"> ( ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">c</font> implies <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> ) &amp;  not  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">d</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">x</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; (  not <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> ) ) )</span><br/><div><span class="kw">hereby </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"> ( ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">c</font> implies <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> ) &amp;  not  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">d</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">x</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; (  not <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> ) ) )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:64_1_1"/>
( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</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="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> or <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> )</span><br/><a NAME="E2:64_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">p9</font>,<font color="Maroon" title="c22">q9</font> &amp; <font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">r9</font>,<font color="Maroon" title="c24">s9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><a NAME="E3:64_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c21">p9</font>,<font color="Maroon" title="c22">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">r9</font>,<font color="Maroon" title="c24">s9</font> or <font color="Maroon" title="c17">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="diraf.html#T46" onmouseover="rs('diraf/T46')" onmouseout="rh()">DIRAF:46</a></span>;<br/><span class="kw">hence </span><a NAME="E4:64_1_1"/>
( <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> or <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</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/></div>
<span class="kw">end;</span></div><div><span class="kw">hereby </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"> (  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> ) &amp;  not  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">d</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">x</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; (  not <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> ) ) )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:64_1_2"/>
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">c</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="c10">b</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font></span><br/><a NAME="E2:64_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c19">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><a NAME="E3:64_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c17">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c19">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="diraf.html#T46" onmouseover="rs('diraf/T46')" onmouseout="rh()">DIRAF:46</a></span>;<br/><span class="kw">hence </span><a NAME="E4:64_1_2"/>
<font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</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/></div>
<span class="kw">end;</span></div><span class="kw">reconsider </span><font color="Maroon" title="c26">x</font> = <font color="Maroon" title="c25">x9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><span class="kw">consider </span><font color="Maroon" title="c27">x9</font>, <font color="Maroon" title="c28">y9</font>, <font color="Maroon" title="c29">z9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #)<span class="kw"> such that </span><br/><a NAME="E13:64_1"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
 not <font color="Maroon" title="c27">x9</font>,<font color="Maroon" title="c28">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">x9</font>,<font color="Maroon" title="c29">z9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="diraf.html#T46" onmouseover="rs('diraf/T46')" onmouseout="rh()">DIRAF:46</a></span>;<br/><a NAME="E14:64_1"/>
( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c26">x</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c26">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:64_1"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">hence </span><a NAME="E15:64_1"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c11">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</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"> (  not  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">d</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">x</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; (  not <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> ) ) )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c30">x</font> = <font color="Maroon" title="c27">x9</font>, <font color="Maroon" title="c31">y</font> = <font color="Maroon" title="c28">y9</font>, <font color="Maroon" title="c32">z</font> = <font color="Maroon" title="c29">z9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><span class="kw">consider </span><font color="Maroon" title="c33">x9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #)<span class="kw"> such that </span><br/><a NAME="E18:64_1"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
<font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c9</font>,<font color="Maroon" title="c33">x9</font>
 <span class="kw">and </span><br/><a NAME="E19:64_1"/><span class="lab"><font color="Green" title="E50">A5</font></span>: 
<font color="Maroon" title="c19">c9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="diraf.html#T46" onmouseover="rs('diraf/T46')" onmouseout="rh()">DIRAF:46</a></span>;<br/><a NAME="E20:64_1"/>
 not <font color="Maroon" title="c30">x</font>,<font color="Maroon" title="c31">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c30">x</font>,<font color="Maroon" title="c32">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:64_1"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">hence </span><a NAME="E21:64_1"/>
 not  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</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"> (  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">d</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">x</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; (  not <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> ) ) )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c34">x</font> = <font color="Maroon" title="c33">x9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><a NAME="E23:64_1"/>
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c34">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:64_1"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">hence </span><a NAME="E24:64_1"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:64_1"><span class="lab"><font color="Green" title="E50">A5</font></span></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"> ( ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">d</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">x</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; (  not <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> ) ) )</span><br/><div><span class="kw">hereby </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"> ( ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) &amp; (  not <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> ) ) )</span>
<div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:64_1_3"/><span class="lab"><font color="Green" title="E51">A6</font></span>: 
<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">and </span><br/><a NAME="E2:64_1_3"/><span class="lab"><font color="Green" title="E52">A7</font></span>: 
<font color="Maroon" title="c10">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a</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">  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">x</font> )</span><br/><a NAME="E3:64_1_3"/>
<font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">d9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1_3"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c35">x9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #)<span class="kw"> such that </span><br/><a NAME="E5:64_1_3"/><span class="lab"><font color="Green" title="E53">A8</font></span>: 
( <font color="Maroon" title="c19">c9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c35">x9</font> &amp; <font color="Maroon" title="c19">c9</font>,<font color="Maroon" title="c17">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">d9</font>,<font color="Maroon" title="c35">x9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E2:64_1_3"><span class="lab"><font color="Green" title="E52">A7</font></span></a>, <a class="ref" href="diraf.html#T46" onmouseover="rs('diraf/T46')" onmouseout="rh()">DIRAF:46</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c36">x</font> = <font color="Maroon" title="c35">x9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><a NAME="E7:64_1_3"/>
( <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c36">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c36">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:64_1_3"><span class="lab"><font color="Green" title="E53">A8</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">hence </span><a NAME="E8:64_1_3"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c9">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">x</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"> verum</span><br/></div>
<span class="kw">end;</span></div><span class="kw">thus </span><a NAME="E26:64_1"/>
( ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> ) ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp; ( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> &amp; <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> &amp;  not <font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c14">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">r</font>,<font color="Maroon" title="c16">s</font> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1"><span class="lab"><font color="Green" title="E46">A1</font></span></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"> (  not <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> ) )</span><br/><span class="kw">assume </span><a NAME="E27:64_1"/>
 not <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</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">  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</font> )</span><br/><a NAME="E28:64_1"/><span class="kw">then </span>
 not <font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c9</font>,<font color="Maroon" title="c20">d9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c35">x9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #)<span class="kw"> such that </span><br/><a NAME="E30:64_1"/><span class="lab"><font color="Green" title="E51">A9</font></span>: 
( <font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">a9</font>,<font color="Maroon" title="c35">x9</font> &amp; <font color="Maroon" title="c19">c9</font>,<font color="Maroon" title="c20">d9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c9</font>,<font color="Maroon" title="c35">x9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="diraf.html#T46" onmouseover="rs('diraf/T46')" onmouseout="rh()">DIRAF:46</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c36">x</font> = <font color="Maroon" title="c35">x9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><a NAME="E32:64_1"/>
( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c36">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c36">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:64_1"><span class="lab"><font color="Green" title="E51">A9</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">hence </span><a NAME="E33:64_1"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">c</font>,<font color="Olive" title="b1">x</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"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">given </span><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font><span class="kw"> such that </span><a NAME="E3:64"/><span class="lab"><font color="Green" title="E46">A10</font></span>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b</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"> (  ex <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 <font color="Maroon" title="c7">POS</font> st <br/>( <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="b2">b</font>,<font color="Olive" title="b1">a</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="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="analoaf.html#R2" title="ANALOAF:pred.2">//</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="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> ) &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="b1">a</font>,<font color="Olive" title="b3">c</font> implies <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> ) &amp;  not  for <font color="Olive" title="b9">x</font>, <font color="Olive" title="b10">y</font>, <font color="Olive" title="b11">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b9">x</font>,<font color="Olive" title="b10">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">x</font>,<font color="Olive" title="b11">z</font> &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">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="b9">x</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="b2">b</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b9">x</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="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> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> 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="b9">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="b9">x</font> ) implies (  not <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="b3">c</font>,<font color="Olive" title="b4">d</font> &amp; (  for <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>  holds <br/>(  not <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="b1">a</font>,<font color="Olive" title="b9">x</font> or  not <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b9">x</font> ) ) ) ) or <font color="Maroon" title="c7">POS</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">OrtAfPl-like</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E4:64"/><span class="lab"><font color="Green" title="E47">A11</font></span>: 
 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 <font color="Maroon" title="c7">POS</font> holds <br/> ( <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="b2">b</font>,<font color="Olive" title="b1">a</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="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="analoaf.html#R2" title="ANALOAF:pred.2">//</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="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> ) &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="b1">a</font>,<font color="Olive" title="b3">c</font> implies <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> ) &amp;  not  for <font color="Olive" title="b9">x</font>, <font color="Olive" title="b10">y</font>, <font color="Olive" title="b11">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> holds  <font color="Olive" title="b9">x</font>,<font color="Olive" title="b10">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">x</font>,<font color="Olive" title="b11">z</font> &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b3">c</font>,<font color="Olive" title="b9">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="b9">x</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="b2">b</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b9">x</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="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> ) &amp;  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> 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="b9">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="b9">x</font> ) &amp; (  not <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="b3">c</font>,<font color="Olive" title="b4">d</font> implies  ex <font color="Olive" title="b9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> st <br/>( <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="b1">a</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b9">x</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="c7">POS</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">OrtAfPl-like</a> </span><br/>

<div><span class="lab"><font color="Green" title="E48">A12</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="64_2"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #)  ex <font color="Olive" title="b4">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b4">t</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">t</font> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c13">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</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">  ex <font color="Olive" title="b1">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Olive" title="b1">t</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">t</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c14">x9</font> = <font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c15">y9</font> = <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c16">z9</font> = <font color="Maroon" title="c13">z</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><span class="kw">consider </span><font color="Maroon" title="c17">t9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font><span class="kw"> such that </span><br/><a NAME="E3:64_2"/><span class="lab"><font color="Green" title="E49">A13</font></span>: 
<font color="Maroon" title="c14">x9</font>,<font color="Maroon" title="c16">z9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">y9</font>,<font color="Maroon" title="c17">t9</font>
 <span class="kw">and </span><br/><a NAME="E4:64_2"/><span class="lab"><font color="Green" title="E50">A14</font></span>: 
<font color="Maroon" title="c15">y9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">t9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E47">A11</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c18">t</font> = <font color="Maroon" title="c17">t9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) ;<br/><a NAME="E6:64_2"/>
<font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c18">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:64_2"><span class="lab"><font color="Green" title="E49">A13</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">hence </span><a NAME="E7:64_2"/>
 ex <font color="Olive" title="b1">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Olive" title="b1">t</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">t</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64_2"><span class="lab"><font color="Green" title="E50">A14</font></span></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/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E49">A15</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="64_3"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font>, <font color="Olive" title="b4">t</font>, <font color="Olive" title="b5">u</font>, <font color="Olive" title="b6">w</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) holds <br/> ( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b3">z</font> &amp; ( <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> &amp; <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">u</font>,<font color="Olive" title="b6">w</font> implies <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">u</font>,<font color="Olive" title="b6">w</font> ) &amp; ( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> implies <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> ) )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c13">z</font>, <font color="Maroon" title="c14">t</font>, <font color="Maroon" title="c15">u</font>, <font color="Maroon" title="c16">w</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</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="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c13">z</font> &amp; ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">y</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">u</font>,<font color="Maroon" title="c16">w</font> implies <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">u</font>,<font color="Maroon" title="c16">w</font> ) &amp; ( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font> implies <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</font> ) )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c17">a</font> = <font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c18">b</font> = <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c19">c</font> = <font color="Maroon" title="c13">z</font>, <font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c14">t</font>, <font color="Maroon" title="c21">e</font> = <font color="Maroon" title="c15">u</font>, <font color="Maroon" title="c22">f</font> = <font color="Maroon" title="c16">w</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><a NAME="E2:64_3"/>
( <font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b</font>,<font color="Maroon" title="c17">a</font> &amp; <font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c</font>,<font color="Maroon" title="c19">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E47">A11</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:64_3"/>
( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c13">z</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</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"> ( ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">y</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">u</font>,<font color="Maroon" title="c16">w</font> implies <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">u</font>,<font color="Maroon" title="c16">w</font> ) &amp; ( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font> implies <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</font> ) )</span><br/><span class="kw">thus </span><a NAME="E4:64_3"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">y</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">u</font>,<font color="Maroon" title="c16">w</font> implies <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">u</font>,<font color="Maroon" title="c16">w</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="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font> implies <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="64_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:64_3_1"/><span class="lab"><font color="Green" title="E50">A16</font></span>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">y</font>
 <span class="kw">and </span><br/><a NAME="E2:64_3_1"/><span class="lab"><font color="Green" title="E51">A17</font></span>: 
( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">u</font>,<font color="Maroon" title="c16">w</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="c13">z</font>,<font color="Maroon" title="c14">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">u</font>,<font color="Maroon" title="c16">w</font></span><br/>

<a NAME="E3:64_3_1"/>
( <font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c</font>,<font color="Maroon" title="c20">d</font> &amp; <font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">e</font>,<font color="Maroon" title="c22">f</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:64_3_1"><span class="lab"><font color="Green" title="E51">A17</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<a NAME="E4:64_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">c</font>,<font color="Maroon" title="c20">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">e</font>,<font color="Maroon" title="c22">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E47">A11</font></span></a>, <a class="txt" href="#E1:64_3_1"><span class="lab"><font color="Green" title="E50">A16</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:64_3_1"/>
<font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">u</font>,<font color="Maroon" title="c16">w</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</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/>


</div><span class="kw">end;</span></div><span class="kw">thus </span><a NAME="E5:64_3"/>
( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font> implies <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</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"> verum</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="64_3_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:64_3_2"/>
<font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</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="c12">y</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</font></span><br/>

<a NAME="E2:64_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c19">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<a NAME="E3:64_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c18">b</font>,<font color="Maroon" title="c17">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b</font>,<font color="Maroon" title="c19">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E47">A11</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:64_3_2"/>
<font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</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/>


</div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E50">A18</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="64_4"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font>, <font color="Olive" title="b4">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #)  st  not <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> holds <br/> ex <font color="Olive" title="b5">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b5">u</font> &amp; <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b5">u</font> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c13">z</font>, <font color="Maroon" title="c14">t</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</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"> (  not <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> implies  ex <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Olive" title="b1">u</font> ) )</span><br/><span class="kw">assume </span><a NAME="E1:64_4"/><span class="lab"><font color="Green" title="E51">A19</font></span>: 
 not <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</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">  ex <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Olive" title="b1">u</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c15">x9</font> = <font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c16">y9</font> = <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c17">z9</font> = <font color="Maroon" title="c13">z</font>, <font color="Maroon" title="c18">t9</font> = <font color="Maroon" title="c14">t</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><a NAME="E3:64_4"/>
 not <font color="Maroon" title="c15">x9</font>,<font color="Maroon" title="c16">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">z9</font>,<font color="Maroon" title="c18">t9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_4"><span class="lab"><font color="Green" title="E51">A19</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c19">u9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font><span class="kw"> such that </span><br/><a NAME="E5:64_4"/><span class="lab"><font color="Green" title="E52">A20</font></span>: 
( <font color="Maroon" title="c15">x9</font>,<font color="Maroon" title="c16">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">x9</font>,<font color="Maroon" title="c19">u9</font> &amp; <font color="Maroon" title="c17">z9</font>,<font color="Maroon" title="c18">t9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">z9</font>,<font color="Maroon" title="c19">u9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E47">A11</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c20">u</font> = <font color="Maroon" title="c19">u9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) ;<br/><a NAME="E7:64_4"/>
( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c20">u</font> &amp; <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c20">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:64_4"><span class="lab"><font color="Green" title="E52">A20</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">hence </span><a NAME="E8:64_4"/>
 ex <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c14">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Olive" title="b1">u</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"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E51">A21</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="64_5"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font>, <font color="Olive" title="b4">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #)  st <font color="Olive" title="b3">z</font>,<font color="Olive" title="b1">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b4">t</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> holds <br/> ex <font color="Olive" title="b5">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b5">u</font> &amp; <font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">t</font>,<font color="Olive" title="b5">u</font> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c13">z</font>, <font color="Maroon" title="c14">t</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</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="c13">z</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c14">t</font> &amp; <font color="Maroon" title="c11">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">z</font> implies  ex <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">t</font>,<font color="Olive" title="b1">u</font> ) )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:64_5"/><span class="lab"><font color="Green" title="E52">A22</font></span>: 
<font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c14">t</font>
 <span class="kw">and </span><br/><a NAME="E2:64_5"/><span class="lab"><font color="Green" title="E53">A23</font></span>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">z</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">  ex <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">t</font>,<font color="Olive" title="b1">u</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c15">x9</font> = <font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c16">y9</font> = <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c17">z9</font> = <font color="Maroon" title="c13">z</font>, <font color="Maroon" title="c18">t9</font> = <font color="Maroon" title="c14">t</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><a NAME="E4:64_5"/>
<font color="Maroon" title="c17">z9</font>,<font color="Maroon" title="c15">x9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">x9</font>,<font color="Maroon" title="c18">t9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_5"><span class="lab"><font color="Green" title="E52">A22</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c19">u9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font><span class="kw"> such that </span><br/><a NAME="E6:64_5"/><span class="lab"><font color="Green" title="E54">A24</font></span>: 
( <font color="Maroon" title="c16">y9</font>,<font color="Maroon" title="c15">x9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">x9</font>,<font color="Maroon" title="c19">u9</font> &amp; <font color="Maroon" title="c16">y9</font>,<font color="Maroon" title="c17">z9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">t9</font>,<font color="Maroon" title="c19">u9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E47">A11</font></span></a>, <a class="txt" href="#E2:64_5"><span class="lab"><font color="Green" title="E53">A23</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c20">u</font> = <font color="Maroon" title="c19">u9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) ;<br/><a NAME="E8:64_5"/>
( <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c20">u</font> &amp; <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">t</font>,<font color="Maroon" title="c20">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:64_5"><span class="lab"><font color="Green" title="E54">A24</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">hence </span><a NAME="E9:64_5"/>
 ex <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">t</font>,<font color="Olive" title="b1">u</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"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E52">A25</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="64_6"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #)  ex <font color="Olive" title="b4">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> &amp; <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b4">t</font> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c13">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</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">  ex <font color="Olive" title="b1">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Olive" title="b1">t</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Olive" title="b1">t</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c14">x9</font> = <font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c15">y9</font> = <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c16">z9</font> = <font color="Maroon" title="c13">z</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> ;<br/><span class="kw">consider </span><font color="Maroon" title="c17">t9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font><span class="kw"> such that </span><br/><a NAME="E3:64_6"/><span class="lab"><font color="Green" title="E53">A26</font></span>: 
( <font color="Maroon" title="c14">x9</font>,<font color="Maroon" title="c15">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">z9</font>,<font color="Maroon" title="c17">t9</font> &amp; <font color="Maroon" title="c14">x9</font>,<font color="Maroon" title="c16">z9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">y9</font>,<font color="Maroon" title="c17">t9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E47">A11</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c18">t</font> = <font color="Maroon" title="c17">t9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) ;<br/><a NAME="E5:64_6"/>
( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c18">t</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c18">t</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:64_6"><span class="lab"><font color="Green" title="E53">A26</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><span class="kw">hence </span><a NAME="E6:64_6"/>
 ex <font color="Olive" title="b1">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) st <br/>( <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">z</font>,<font color="Olive" title="b1">t</font> &amp; <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">y</font>,<font color="Olive" title="b1">t</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"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E10:64"/>
 not  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="64_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c13">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font><span class="kw"> such that </span><br/><a NAME="E2:64_7"/><span class="lab"><font color="Green" title="E53">A27</font></span>: 
 not <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c13">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E47">A11</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">x9</font> = <font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c15">y9</font> = <font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c16">z9</font> = <font color="Maroon" title="c13">z</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) ;<br/>
<a NAME="E4:64_7"/>
 not <font color="Maroon" title="c14">x9</font>,<font color="Maroon" title="c15">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">x9</font>,<font color="Maroon" title="c16">z9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:64_7"><span class="lab"><font color="Green" title="E53">A27</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:64_7"/>
 not  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</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"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E11:64"/>
 <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="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) is   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:64"><span class="lab"><font color="Green" title="E46">A10</font></span></a>, <a class="txt" href="#E6:64"><span class="lab"><font color="Green" title="E49">A15</font></span></a>, <a class="txt" href="#E5:64"><span class="lab"><font color="Green" title="E48">A12</font></span></a>, <a class="txt" href="#E9:64"><span class="lab"><font color="Green" title="E52">A25</font></span></a>, <a class="txt" href="#E8:64"><span class="lab"><font color="Green" title="E51">A21</font></span></a>, <a class="txt" href="#E7:64"><span class="lab"><font color="Green" title="E50">A18</font></span></a>, <a class="ref" href="diraf.html#T46" onmouseover="rs('diraf/T46')" onmouseout="rh()">DIRAF:46</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="analmetr.html#D9" target="_self" onmouseover="rs('analmetr/D9')" onmouseout="rh()">ANALMETR:def 9</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">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 <font color="Maroon" title="c7">POS</font> 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> ) ) ) &amp; (  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 <font color="Maroon" title="c7">POS</font>  ex <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> 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> ) ) )</span><br/>

<span class="kw">thus </span><a NAME="E12:64"/>
 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 <font color="Maroon" title="c7">POS</font> 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> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E47">A11</font></span></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">  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 <font color="Maroon" title="c7">POS</font>  ex <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> 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> )</span><br/>

<span class="kw">thus </span><a NAME="E13:64"/>
 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 <font color="Maroon" title="c7">POS</font>  ex <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font> 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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E47">A11</font></span></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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