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<span class="kw">let </span><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:()"><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 <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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>



<span class="kw">assume </span><a NAME="E1:11"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
 <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">x9</font> = <font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c6">y9</font> = <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c7">z9</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<a NAME="E3:11"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">x9</font>,<font color="Maroon" title="c6">y9</font>,<font color="Maroon" title="c7">z9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E4:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A3</font></span>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">y9</font>,<font color="Maroon" title="c7">z9</font>,<font color="Maroon" title="c5">x9</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">z9</font>,<font color="Maroon" title="c5">x9</font>,<font color="Maroon" title="c6">y9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E5:11"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">z9</font>,<font color="Maroon" title="c6">y9</font>,<font color="Maroon" title="c5">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E6:11"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">x9</font>,<font color="Maroon" title="c7">z9</font>,<font color="Maroon" title="c6">y9</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">y9</font>,<font color="Maroon" title="c5">x9</font>,<font color="Maroon" title="c7">z9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:11"/>
(  <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E5:11"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>; <a class="txt" 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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