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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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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><br/> for <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a9</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">c9</font> holds <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> iff  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font>,<font color="Olive" title="b6">c9</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c10">c</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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a9</font>, <font color="Olive" title="b2">b9</font>, <font color="Olive" title="b3">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span>  st <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a9</font> &amp; <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b9</font> &amp; <font color="Maroon" title="c10">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c9</font> holds <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">c</font> iff  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">a9</font>,<font color="Olive" title="b2">b9</font>,<font color="Olive" title="b3">c9</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c11">a9</font>, <font color="Maroon" title="c12">b9</font>, <font color="Maroon" title="c13">c9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a9</font> &amp; <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b9</font> &amp; <font color="Maroon" title="c10">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c9</font> implies (  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">c</font> iff  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">a9</font>,<font color="Maroon" title="c12">b9</font>,<font color="Maroon" title="c13">c9</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:83"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
( <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a9</font> &amp; <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b9</font> &amp; <font color="Maroon" title="c10">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c9</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">c</font> iff  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">a9</font>,<font color="Maroon" title="c12">b9</font>,<font color="Maroon" title="c13">c9</font> )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">a9</font>,<font color="Maroon" title="c12">b9</font>,<font color="Maroon" title="c13">c9</font> implies  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">c</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:83_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">a9</font>,<font color="Maroon" title="c12">b9</font>,<font color="Maroon" title="c13">c9</font></span><br/><a NAME="E2:83_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c10">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" target="_self" title="ANALMETR:def.11">Def11</a></span>;<br/><a NAME="E3:83_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">a9</font>,<font color="Maroon" title="c12">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a9</font>,<font color="Maroon" title="c13">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/><span class="kw">hence </span><a NAME="E4:83_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">a9</font>,<font color="Maroon" title="c12">b9</font>,<font color="Maroon" title="c13">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E3:83"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">a9</font>,<font color="Maroon" title="c12">b9</font>,<font color="Maroon" title="c13">c9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">c</font></span><br/>

<a NAME="E4:83"/><span class="kw">then </span>
<font color="Maroon" title="c11">a9</font>,<font color="Maroon" title="c12">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a9</font>,<font color="Maroon" title="c13">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E5:83"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c10">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:83"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" target="_self" title="ANALMETR:def.11">Def11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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