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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">H1</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>, <font color="Maroon">H2</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">h1</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="group_4.html#K11">lattice</a> <font color="Maroon">G</font></span>)</span>, <font color="Maroon">h2</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="group_4.html#K11">lattice</a> <font color="Maroon">G</font></span>)</span>;<br/>





<a NAME="E1:23"/><i><font color="Green">E23</font></i>: 
 <a href="group_4.html#K11">lattice</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9">SubJoin</a> <font color="Maroon">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10">SubMeet</a> <font color="Maroon">G</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="group_4.html#D13">GROUP_4:def 13</a></i>;<br/>
<a NAME="E2:23"/><b>then </b>
<font color="Maroon">h1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">h2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_4.html#K9">SubJoin</a> <font color="Maroon">G</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">h1</font>,<font color="Maroon">h2</font>
 
<b>by </b><i><a class="ref" href="lattices.html#D1">LATTICES:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:23"/>
( <font color="Maroon">h1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H1</font> &amp; <font color="Maroon">h2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H2</font> implies <font color="Maroon">h1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">h2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H1</font> <a href="group_4.html#K8">"\/"</a> <font color="Maroon">H2</font> )
 <b>by </b><i>, <a class="ref" href="group_4.html#D11">GROUP_4:def 11</a></i>;<br/>


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