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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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"> ( ( <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> or <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> ) implies for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">X</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> &amp; <font color="Olive" title="b1">X</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> &amp; <font color="Olive" title="b2">Y</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> &amp; <font color="Olive" title="b2">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> holds <br/><font color="Olive" title="b1">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> )</span><br/>

<b>assume </b><a NAME="E1:84"/><i><font color="Green" title="E43">A1</font></i>: 
( <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> or <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</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>, <font color="Olive" title="b2">Y</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">X</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> &amp; <font color="Olive" title="b1">X</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> &amp; <font color="Olive" title="b2">Y</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> &amp; <font color="Olive" title="b2">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> holds <br/><font color="Olive" title="b1">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a></span><br/>

<b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">X</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> &amp; <font color="Maroon" title="c2">X</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> &amp; <font color="Maroon" title="c3">Y</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> &amp; <font color="Maroon" title="c3">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> implies <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E2:84"/><i><font color="Green" title="E44">A2</font></i>: 
( <font color="Maroon" title="c2">X</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> &amp; <font color="Maroon" title="c2">X</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> )
 <b>and </b><br/><a NAME="E3:84"/><i><font color="Green" title="E45">A3</font></i>: 
( <font color="Maroon" title="c3">Y</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> &amp; <font color="Maroon" title="c3">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a></span><br/>

<a NAME="E4:84"/><i><font color="Green" title="E46">A4</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a>
 
<b>by </b><i><a class="txt" href="#E2:84"><i><font color="Green" title="E44">A2</font></i></a>, <a class="txt" href="#E3:84"><i><font color="Green" title="E45">A3</font></i></a>, <a class="ref" href="waybel_0.html#T27" target="_self" title="WAYBEL_0:th.27">Th27</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:84_1"/>
( <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> or <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> )
 </span><b>by </b><i><a class="txt" href="#E1:84"><i><font color="Green" title="E43">A1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_1"><b>suppose </b></a><a NAME="E1:84_1_1"/><i><font color="Green" title="E47">A5</font></i>: 
<font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_1_1"><b>now </b></a><div class="add"><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 <font color="Maroon" title="c1">L</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#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> implies <font color="Maroon" title="c4">x</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> )</span><br/><b>assume </b><a NAME="E1:84_1_1_1"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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"> <font color="Maroon" title="c4">x</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font></span><br/><a NAME="E2:84_1_1_1"/><b>then </b>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:84_1_1_1"/><b>then </b>
( <font color="Maroon" title="c4">x</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c4">x</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font> )
 <b>by </b><i><a class="txt" href="#E2:84"><i><font color="Green" title="E44">A2</font></i></a>, <a class="txt" href="#E3:84"><i><font color="Green" title="E45">A3</font></i></a>, <a class="txt" href="#E1:84_1_1"><i><font color="Green" title="E47">A5</font></i></a>, <a class="ref" href="waybel_0.html#T40" target="_self" title="WAYBEL_0:th.40">Th40</a></i>;<br/><b>hence </b><a NAME="E4:84_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <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><b>hence </b><a NAME="E3:84_1_1"/>
<font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>
 <b>by </b><i><a class="txt" href="#E4:84"><i><font color="Green" title="E46">A4</font></i></a>, <a class="txt" href="#E1:84_1_1"><i><font color="Green" title="E47">A5</font></i></a>, <a class="ref" href="waybel_0.html#T40" target="_self" title="WAYBEL_0:th.40">Th40</a></i>; <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="84_1_2"><b>suppose </b></a><a NAME="E1:84_1_2"/><i><font color="Green" title="E47">A6</font></i>: 
<font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a></span><br/><div class="add"><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 <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D1" target="_self" title="WAYBEL_0:def.1">WAYBEL_0:def 1</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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> implies  ex <font color="Olive" title="b1">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">z</font> &amp; <font color="Maroon" title="c5">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">z</font> ) )</span><br/><b>assume </b><a NAME="E2:84_1_2"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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">  ex <font color="Olive" title="b1">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">z</font> &amp; <font color="Maroon" title="c5">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">z</font> )</span><br/><a NAME="E3:84_1_2"/><b>then </b><i><font color="Green" title="E48">A7</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">zx</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E5:84_1_2"/><i><font color="Green" title="E49">A8</font></i>: 
( <font color="Maroon" title="c6">zx</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">zx</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="c6">zx</font> )
 <b>by </b><i><a class="txt" href="#E2:84"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="waybel_0.html#D1" target="_self" title="WAYBEL_0:def.1">Def1</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">zy</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E7:84_1_2"/><i><font color="Green" title="E50">A9</font></i>: 
( <font color="Maroon" title="c7">zy</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">zy</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="c7">zy</font> )
 <b>by </b><i><a class="txt" href="#E3:84"><i><font color="Green" title="E45">A3</font></i></a>, <a class="txt" href="#E3:84_1_2"><i><font color="Green" title="E48">A7</font></i></a>, <a class="ref" href="waybel_0.html#D1" target="_self" title="WAYBEL_0:def.1">Def1</a></i>;<br/><b>take </b><font color="Maroon" title="c8">z</font> = <font color="Maroon" title="c6">zx</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c7">zy</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c8">z</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="c8">z</font> )</span><br/><a NAME="E8:84_1_2"/>
( <font color="Maroon" title="c8">z</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">zx</font> &amp; <font color="Maroon" title="c8">z</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">zy</font> )
 <b>by </b><i><a class="txt" href="#E1:84_1_2"><i><font color="Green" title="E47">A6</font></i></a>, <a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/><a NAME="E9:84_1_2"/><b>then </b>
( <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font> )
 <b>by </b><i><a class="txt" href="#E2:84"><i><font color="Green" title="E44">A2</font></i></a>, <a class="txt" href="#E3:84"><i><font color="Green" title="E45">A3</font></i></a>, <a class="txt" href="#E5:84_1_2"><i><font color="Green" title="E49">A8</font></i></a>, <a class="txt" href="#E7:84_1_2"><i><font color="Green" title="E50">A9</font></i></a>, <a class="ref" href="waybel_0.html#D19" target="_self" title="WAYBEL_0:def.19">Def19</a></i>;<br/><b>hence </b><a NAME="E10:84_1_2"/>
<font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Y</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <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="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c8">z</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="c8">z</font> )</span><br/><b>thus </b><a NAME="E11:84_1_2"/>
( <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c8">z</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="c8">z</font> )
 <b>by </b><i><a class="txt" href="#E1:84_1_2"><i><font color="Green" title="E47">A6</font></i></a>, <a class="txt" href="#E5:84_1_2"><i><font color="Green" title="E49">A8</font></i></a>, <a class="txt" href="#E7:84_1_2"><i><font color="Green" title="E50">A9</font></i></a>, <a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>; <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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