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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V2">with_infima</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:17_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">L</font> is <a href="waybel_1.html#V2">distributive</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>assume </b><a NAME="E1:17_1_1_1"/>
<font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c</font>
 ;<br/><b>hence </b><font color="Maroon">a</font> <a href="lattice3.html#K10">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font></span>)</span> <a href="lattice3.html#K10">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">b</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="waybel_1.html#D3">WAYBEL_1:def 3</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:17_1_1"/>
<font color="Maroon">L</font> is <a href="yellow11.html#V1" target="_self">modular</a>
 <b>by </b><i/>;<br/>


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