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<span class="kw">let </span><font color="Maroon" title="c7">POS</font> be   <a href="analmetr.html#NM1" title="ANALMETR:NM.1">OrtAfSp</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">M</font>, <font color="Olive" title="b2">N</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">POS</font><br/>  for <font color="Olive" title="b3">M9</font>, <font color="Olive" title="b4">N9</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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="b1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">M9</font> &amp; <font color="Olive" title="b2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">N9</font> holds <br/>( <font color="Olive" title="b1">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Olive" title="b2">N</font> iff <font color="Olive" title="b3">M9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Olive" title="b4">N9</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">M</font>, <font color="Maroon" title="c9">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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">  for <font color="Olive" title="b1">M9</font>, <font color="Olive" title="b2">N9</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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="Maroon" title="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M9</font> &amp; <font color="Maroon" title="c9">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">N9</font> holds <br/>( <font color="Maroon" title="c8">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c9">N</font> iff <font color="Olive" title="b1">M9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Olive" title="b2">N9</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c10">M9</font>, <font color="Maroon" title="c11">N9</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">M9</font> &amp; <font color="Maroon" title="c9">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">N9</font> implies ( <font color="Maroon" title="c8">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c9">N</font> iff <font color="Maroon" title="c10">M9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N9</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:76"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
( <font color="Maroon" title="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">M9</font> &amp; <font color="Maroon" title="c9">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">N9</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="c8">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c9">N</font> iff <font color="Maroon" title="c10">M9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N9</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="c10">M9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N9</font> implies <font color="Maroon" title="c8">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c9">N</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:76_1"/>
<font color="Maroon" title="c8">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c9">N</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">M9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N9</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">a</font>, <font color="Maroon" title="c13">b</font>, <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c15">d</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="E3:76_1"/><span class="lab"><font color="Green" title="E55">A2</font></span>: 
( <font color="Maroon" title="c12">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b</font> &amp; <font color="Maroon" title="c14">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">d</font> )
 <span class="kw">and </span><br/><a NAME="E4:76_1"/><span class="lab"><font color="Green" title="E56">A3</font></span>: 
( <font color="Maroon" title="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">b</font>) &amp; <font color="Maroon" title="c9">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c15">d</font>) )
 <span class="kw">and </span><br/><a NAME="E5:76_1"/><span class="lab"><font color="Green" title="E57">A4</font></span>: 
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c15">d</font>
 ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c16">a9</font> = <font color="Maroon" title="c12">a</font>, <font color="Maroon" title="c17">b9</font> = <font color="Maroon" title="c13">b</font>, <font color="Maroon" title="c18">c9</font> = <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c19">d9</font> = <font color="Maroon" title="c15">d</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="E7:76_1"/><span class="lab"><font color="Green" title="E58">A5</font></span>: 
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c9</font>,<font color="Maroon" title="c19">d9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:76_1"><span class="lab"><font color="Green" title="E57">A4</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/><a NAME="E8:76_1"/>
( <font color="Maroon" title="c10">M9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font>) &amp; <font color="Maroon" title="c11">N9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c18">c9</font>,<font color="Maroon" title="c19">d9</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E4:76_1"><span class="lab"><font color="Green" title="E56">A3</font></span></a>, <a class="ref" href="analmetr.html#T41" target="_self" onmouseover="rs('analmetr/T41')" onmouseout="rh()">Th41</a></span>;<br/><span class="kw">hence </span><a NAME="E9:76_1"/>
<font color="Maroon" title="c10">M9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:76_1"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="txt" href="#E7:76_1"><span class="lab"><font color="Green" title="E58">A5</font></span></a>, <a class="ref" href="aff_1.html#T37" onmouseover="rs('aff_1/T37')" onmouseout="rh()">AFF_1:37</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">assume </span><a NAME="E3:76"/>
<font color="Maroon" title="c10">M9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N9</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="c8">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c9">N</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">a9</font>, <font color="Maroon" title="c13">b9</font>, <font color="Maroon" title="c14">c9</font>, <font color="Maroon" title="c15">d9</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="E5:76"/><span class="lab"><font color="Green" title="E55">A6</font></span>: 
( <font color="Maroon" title="c12">a9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b9</font> &amp; <font color="Maroon" title="c14">c9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">d9</font> )
 <span class="kw">and </span><br/><a NAME="E6:76"/><span class="lab"><font color="Green" title="E56">A7</font></span>: 
<font color="Maroon" title="c12">a9</font>,<font color="Maroon" title="c13">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c9</font>,<font color="Maroon" title="c15">d9</font>
 <span class="kw">and </span><br/><a NAME="E7:76"/><span class="lab"><font color="Green" title="E57">A8</font></span>: 
( <font color="Maroon" title="c10">M9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c12">a9</font>,<font color="Maroon" title="c13">b9</font>) &amp; <font color="Maroon" title="c11">N9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c14">c9</font>,<font color="Maroon" title="c15">d9</font>) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T37" onmouseover="rs('aff_1/T37')" onmouseout="rh()">AFF_1:37</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">a</font> = <font color="Maroon" title="c12">a9</font>, <font color="Maroon" title="c17">b</font> = <font color="Maroon" title="c13">b9</font>, <font color="Maroon" title="c18">c</font> = <font color="Maroon" title="c14">c9</font>, <font color="Maroon" title="c19">d</font> = <font color="Maroon" title="c15">d9</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="E9:76"/><span class="lab"><font color="Green" title="E58">A9</font></span>: 
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:76"><span class="lab"><font color="Green" title="E56">A7</font></span></a>, <a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<a NAME="E10:76"/>
( <font color="Maroon" title="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>) &amp; <font color="Maroon" title="c9">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">d</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E7:76"><span class="lab"><font color="Green" title="E57">A8</font></span></a>, <a class="ref" href="analmetr.html#T41" target="_self" onmouseover="rs('analmetr/T41')" onmouseout="rh()">Th41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:76"/>
<font color="Maroon" title="c8">M</font> <a href="analmetr.html#R8" title="ANALMETR:pred.8">//</a> <font color="Maroon" title="c9">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:76"><span class="lab"><font color="Green" title="E55">A6</font></span></a>, <a class="txt" href="#E9:76"><span class="lab"><font color="Green" title="E58">A9</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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