<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">MP</font> be   <a href="analmetr.html#NM1" title="ANALMETR:NM.1">OrtAfSp</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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 <font color="Maroon" title="c1">MP</font>  st  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> holds <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font>,<font color="Olive" title="b2">y</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font> )</span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> implies (  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> ) )</span><br/>



<b>assume </b><a NAME="E1:11"/><i><font color="Green" title="E11">A1</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c5">x'</font> = <font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c6">y'</font> = <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c7">z'</font> = <font color="Maroon" title="c4">z</font> as   <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="c1">MP</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:11"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">x'</font>,<font color="Maroon" title="c6">y'</font>,<font color="Maroon" title="c7">z'</font>
 
<b>by </b><i><a class="txt" href="#E1:11"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:11"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">x'</font>,<font color="Maroon" title="c7">z'</font>,<font color="Maroon" title="c6">y'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">y'</font>,<font color="Maroon" title="c5">x'</font>,<font color="Maroon" title="c7">z'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">y'</font>,<font color="Maroon" title="c7">z'</font>,<font color="Maroon" title="c5">x'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">z'</font>,<font color="Maroon" title="c5">x'</font>,<font color="Maroon" title="c6">y'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">z'</font>,<font color="Maroon" title="c6">y'</font>,<font color="Maroon" title="c5">x'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E5:11"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
