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<b>let </b><font color="Maroon" title="c1">V</font>, <font color="Maroon" title="c2">C</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>;<br/>





<b>reconsider </b><font color="Maroon" title="c6">a'</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c7">b'</font> = <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c8">c'</font> = <font color="Maroon" title="c5">c</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substlat.html#K1" title="SUBSTLAT:func.1">SubstitutionSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> <b>by </b><i><a class="ref" href="substlat.html#D4" target="_self" title="SUBSTLAT:def.4">Def4</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">G</font> =  <a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font>;<br/>
<font color="Maroon" title="c3">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">c</font></span>)</span> = 
the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">a</font>,<span class="p1">(<span class="default"><a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">b'</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">c'</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#D4" target="_self" title="SUBSTLAT:def.4">Def4</a></i>
<br/>.= 
 <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a'</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p2">(<span class="default"><a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">b'</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">c'</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#D4" target="_self" title="SUBSTLAT:def.4">Def4</a></i>
<br/>.= 
 <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a'</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">b'</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">c'</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#T20" target="_self" title="SUBSTLAT:th.20">Th20</a></i>
<br/>.= 
 <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">a'</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c7">b'</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">c'</font></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#T21" target="_self" title="SUBSTLAT:th.21">Th21</a></i>
<br/>.= 
 <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">a'</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c7">b'</font></span>)</span></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">c'</font></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#T19" target="_self" title="SUBSTLAT:th.19">Th19</a></i>
<br/>.= 
the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">a'</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c7">b'</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">c'</font>
<b>by </b><i><a class="ref" href="substlat.html#D4" target="_self" title="SUBSTLAT:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">c</font>
<b>by </b><i><a class="ref" href="substlat.html#D4" target="_self" title="SUBSTLAT:def.4">Def4</a></i>
;<br/>
<b>hence </b><a NAME="E3:45"/>
<font color="Maroon" title="c3">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">c</font>
 ;<br/>


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