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<span class="kw">let </span><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>; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E1:47_1_1"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
( <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">consider </span><font color="Maroon" title="c6">y1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E3:47_1_1"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<font color="Maroon" title="c6">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font>
 <span class="kw">and </span><br/><a NAME="E4:47_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">y1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_9.html#D7" target="_self" title="WAYBEL_9:def.7">Def7</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">x1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E6:47_1_1"/><span class="lab"><font color="Green" title="E23">A3</font></span>: 
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font>
 <span class="kw">and </span><br/><a NAME="E7:47_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">x1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_9.html#D7" target="_self" title="WAYBEL_9:def.7">Def7</a></span>;<br/>
<a NAME="E8:47_1_1"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_9.html#T14" target="_self" title="WAYBEL_9:th.14">Th14</a></span>;<br/>
<a NAME="E9:47_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c7">x1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">y1</font> &amp; <font color="Maroon" title="c6">y1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">x1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E6:47_1_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="txt" href="#E3:47_1_1"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="yellow_6.html#T20" title="YELLOW_6:th.20">YELLOW_6:20</a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:47_1_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="txt" href="#E3:47_1_1"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="yellow_0.html#D3" title="YELLOW_0:def.3">YELLOW_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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