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<a NAME="E1:12_1_1"/>
 <a href="lattices.html#G3">LattStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="nat_lat.html#K2" target="_self">lcmlat</a> ,<a href="nat_lat.html#K1" target="_self">hcflat</a>  #) is <a href="lattices.html#V10">Lattice-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:12_1_1_1"/>
( ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="nat_lat.html#K2" target="_self">lcmlat</a> ,<a href="nat_lat.html#K1" target="_self">hcflat</a>  #) holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="nat_lat.html#K2" target="_self">lcmlat</a> ,<a href="nat_lat.html#K1" target="_self">hcflat</a>  #) holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="lattices.html#K1">"\/"</a> <font color="Olive">b<sub>3</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="nat_lat.html#K2" target="_self">lcmlat</a> ,<a href="nat_lat.html#K1" target="_self">hcflat</a>  #) holds <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="lattices.html#K1">"\/"</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="nat_lat.html#K2" target="_self">lcmlat</a> ,<a href="nat_lat.html#K1" target="_self">hcflat</a>  #) holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="nat_lat.html#K2" target="_self">lcmlat</a> ,<a href="nat_lat.html#K1" target="_self">hcflat</a>  #) holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="lattices.html#K2">"/\"</a> <font color="Olive">b<sub>3</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="nat_lat.html#K2" target="_self">lcmlat</a> ,<a href="nat_lat.html#K1" target="_self">hcflat</a>  #) holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="nat_lat.html#E55"><i><font color="Green">Lemma5</font></i></a>, <a class="txt" href="nat_lat.html#E56"><i><font color="Green">Lemma6</font></i></a>, <a class="txt" href="nat_lat.html#E57"><i><font color="Green">Lemma7</font></i></a>, <a class="txt" href="nat_lat.html#E58"><i><font color="Green">Lemma8</font></i></a>, <a class="txt" href="nat_lat.html#E59"><i><font color="Green">Lemma9</font></i></a>, <a class="txt" href="nat_lat.html#E60"><i><font color="Green">Lemma10</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D4">LATTICES:def 4</a>,<a class="ref" href="lattices.html#D5">LATTICES:def 5</a>,<a class="ref" href="lattices.html#D6">LATTICES:def 6</a>,<a class="ref" href="lattices.html#D7">LATTICES:def 7</a>,<a class="ref" href="lattices.html#D8">LATTICES:def 8</a>,<a class="ref" href="lattices.html#D9">LATTICES:def 9</a>,<a class="ref" href="lattices.html#D10">LATTICES:def 10</a><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:12_1_1"/>
 <a href="lattices.html#G3">LattStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="nat_lat.html#K2" target="_self">lcmlat</a> ,<a href="nat_lat.html#K1" target="_self">hcflat</a>  #) is   <a href="lattices.html#NM1">Lattice</a>
 ;<br/>


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