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<b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D3" title="YELLOW_0:def.3">YELLOW_0:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">y</font> or  not <font color="Maroon" title="c5">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">x</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> )</span><br/>

<b>assume </b><a NAME="E1:47_1_1"/><i><font color="Green" title="E22">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">y</font> &amp; <font color="Maroon" title="c5">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">x</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font></span><br/>

<a NAME="E2:47_1_1"/><i><font color="Green" title="E23">A2</font></i>: 
<font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font> is    <a href="yellow_6.html#M1" title="YELLOW_6:mode.1">SubNetStr</a> of <font color="Maroon" title="c2">N</font>
 
<b>by </b><i><a class="ref" href="waybel_9.html#T14" target="_self" title="WAYBEL_9:th.14">Th14</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">x1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font><b> such that </b><br/><a NAME="E4:47_1_1"/><i><font color="Green" title="E24">A3</font></i>: 
<font color="Maroon" title="c6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font>
 <b>and </b><br/><a NAME="E5:47_1_1"/>
<font color="Maroon" title="c3">i</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">x1</font>
 <b>by </b><i><a class="ref" href="waybel_9.html#D7" target="_self" title="WAYBEL_9:def.7">Def7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">y1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font><b> such that </b><br/><a NAME="E7:47_1_1"/><i><font color="Green" title="E25">A4</font></i>: 
<font color="Maroon" title="c7">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font>
 <b>and </b><br/><a NAME="E8:47_1_1"/>
<font color="Maroon" title="c3">i</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">y1</font>
 <b>by </b><i><a class="ref" href="waybel_9.html#D7" target="_self" title="WAYBEL_9:def.7">Def7</a></i>;<br/>
<a NAME="E9:47_1_1"/>
( <font color="Maroon" title="c6">x1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">y1</font> &amp; <font color="Maroon" title="c7">y1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">x1</font> )
 
<b>by </b><i><a class="txt" href="waybel_9.html#E1:47_1_1"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="waybel_9.html#E2:47_1_1"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="waybel_9.html#E4:47_1_1"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="waybel_9.html#E7:47_1_1"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="yellow_6.html#T20" title="YELLOW_6:th.20">YELLOW_6:20</a></i>;<br/>
<b>hence </b><a NAME="E10:47_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font>
 <b>by </b><i><a class="txt" href="waybel_9.html#E4:47_1_1"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="waybel_9.html#E7:47_1_1"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="yellow_0.html#D3" title="YELLOW_0:def.3">YELLOW_0:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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