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<b>let </b><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L2</font> #) &amp; <font color="Maroon" title="c1">L1</font> is <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</a> implies for <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="c1">L1</font><br/> for <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b1">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> holds <br/><font color="Olive" title="b2">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green" title="E11">A1</font></i>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L2</font> #)
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green" title="E12">A2</font></i>: 
<font color="Maroon" title="c1">L1</font> is <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <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="c1">L1</font><br/> for <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b1">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> holds <br/><font color="Olive" title="b2">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a></span><br/>

<b>let </b><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> &amp; <font color="Maroon" title="c3">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> holds <br/><font color="Olive" title="b1">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a></span><br/><b>let </b><font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> &amp; <font color="Maroon" title="c3">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> implies <font color="Maroon" title="c4">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E3:22"/><i><font color="Green" title="E13">A3</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font>
 <b>and </b><br/><a NAME="E4:22"/><i><font color="Green" title="E14">A4</font></i>: 
<font color="Maroon" title="c3">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a></span><br/>

<a NAME="E5:22"/>
<font color="Maroon" title="c3">x</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Maroon" title="c3">x</font>
 
<b>by </b><i><a class="txt" href="waybel_8.html#E4:22"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="waybel_3.html#D2" title="WAYBEL_3:def.2">WAYBEL_3:def 2</a></i>;<br/>
<a NAME="E6:22"/><b>then </b>
<font color="Maroon" title="c4">y</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Maroon" title="c4">y</font>
 
<b>by </b><i><a class="txt" href="waybel_8.html#E1:22"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="waybel_8.html#E2:22"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="waybel_8.html#E3:22"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="waybel_8.html#T8" target="_self" title="WAYBEL_8:th.8">Th8</a></i>;<br/>
<b>hence </b><a NAME="E7:22"/>
<font color="Maroon" title="c4">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a>
 <b>by </b><i><a class="ref" href="waybel_3.html#D2" title="WAYBEL_3:def.2">WAYBEL_3:def 2</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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