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<b>consider </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E2:61_1_1"/><i><font color="Green" title="E8">W</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="struct_0.html#D10" target="_self" title="STRUCT_0:def.10">Def10</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:61_1_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">S</font> or <font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">S</font> )
 </span><b>by </b><i><a class="txt" href="#E2:61_1_1"><i><font color="Green" title="E8">W</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_1_1_1"><b>suppose </b></a><a NAME="E1:61_1_1_1_1"/><i><font color="Green" title="E9">S</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V12" title="STRUCT_0:attr.12">zero</a></span><br/><div class="add"><b>take </b>
<font color="Maroon" title="c2">x</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c2">x</font> is <a href="struct_0.html#V12" title="STRUCT_0:attr.12">zero</a></span><br/><b>thus </b><a NAME="E2:61_1_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">S</font>
 <b>by </b><i><a class="txt" href="#E1:61_1_1_1_1"><i><font color="Green" title="E9">S</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D15" target="_self" title="STRUCT_0:def.15">STRUCT_0:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_1_1_2"><b>suppose </b></a><a NAME="E1:61_1_1_1_2"/><i><font color="Green" title="E9">S</font></i>: 
<font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V12" title="STRUCT_0:attr.12">zero</a></span><br/><div class="add"><b>take </b>
<font color="Maroon" title="c3">y</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c3">y</font> is <a href="struct_0.html#V12" title="STRUCT_0:attr.12">zero</a></span><br/><b>thus </b><a NAME="E2:61_1_1_1_2"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">S</font>
 <b>by </b><i><a class="txt" href="#E1:61_1_1_1_2"><i><font color="Green" title="E9">S</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D15" target="_self" title="STRUCT_0:def.15">STRUCT_0:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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