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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L</font> being   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a><br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/>( <font color="Olive" title="b2">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">L</font>) &amp;  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">L</font>) <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">a</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">L</font> be   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>  st <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/>( <font color="Olive" title="b1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>) &amp;  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>) <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b1">a</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font> implies ( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>) &amp;  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>) <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:25"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>) &amp;  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>) <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font> )</span><br/>

<a NAME="E2:25"/>
<font color="Maroon" title="c1">X</font> <a href="lattice3.html#R2" title="LATTICE3:pred.2">is_&lt;=_than</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T32" onmouseover="rs('yellow_0/T32')" onmouseout="rh()">YELLOW_0:32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:25"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E7">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>) <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font></span><br/>

<a NAME="E4:25"/>
<font color="Maroon" title="c1">X</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T33" onmouseover="rs('yellow_0/T33')" onmouseout="rh()">YELLOW_0:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:25"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>) <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E7">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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