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<span class="kw">let </span><font color="Maroon" title="c7">POS</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</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">p</font>, <font color="Olive" title="b3">q</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="b4">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">x</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">p</font>, <font color="Maroon" title="c10">q</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">  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="c8">a</font>,<font color="Olive" title="b1">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font>,<font color="Olive" title="b1">x</font> )</span><br/>







<div><span class="lab"><font color="Green" title="E67">A1</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="101_1"><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"> ( <font color="Maroon" title="c9">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">q</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="c8">a</font>,<font color="Olive" title="b1">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font>,<font color="Olive" title="b1">x</font> ) )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:101_1"/>
<font color="Maroon" title="c9">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">q</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="c8">a</font>,<font color="Olive" title="b1">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font>,<font color="Olive" title="b1">x</font> )</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">x</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="E3:101_1"/><span class="lab"><font color="Green" title="E68">A2</font></span>: 
( <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c11">x</font> &amp; <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c8">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D8" target="_self" onmouseover="rs('analmetr/D8')" onmouseout="rh()">Def7</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c12">x</font> = <font color="Maroon" title="c11">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="c8">a</font>,<font color="Maroon" title="c12">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font>,<font color="Maroon" title="c12">x</font> )</span><br/><span class="kw">thus </span><a NAME="E4:101_1"/>
( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c12">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font>,<font color="Maroon" title="c12">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:101_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="ref" href="analmetr.html#T61" target="_self" onmouseover="rs('analmetr/T61')" onmouseout="rh()">Th61</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><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="101_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"> ( <font color="Maroon" title="c9">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">q</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="c8">a</font>,<font color="Olive" title="b1">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font>,<font color="Olive" title="b1">x</font> ) )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:101_2"/><span class="lab"><font color="Green" title="E68">A3</font></span>: 
<font color="Maroon" title="c9">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">q</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="c8">a</font>,<font color="Olive" title="b1">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font>,<font color="Olive" title="b1">x</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c8">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"> ( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c11">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font>,<font color="Maroon" title="c11">x</font> )</span><br/><a NAME="E2:101_2"/>
<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c8">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:101_2"><span class="lab"><font color="Green" title="E68">A3</font></span></a>, <a class="ref" href="analmetr.html#T58" target="_self" onmouseover="rs('analmetr/T58')" onmouseout="rh()">Th58</a></span>;<br/><span class="kw">hence </span><a NAME="E3:101_2"/>
( <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c11">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font>,<font color="Maroon" title="c11">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T58" target="_self" onmouseover="rs('analmetr/T58')" onmouseout="rh()">Th58</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">hence </span><a NAME="E3:101"/>
 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="c8">a</font>,<font color="Olive" title="b1">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:101"><span class="lab"><font color="Green" title="E67">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"> verum</span><br/>


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