<?xml version="1.0"?>
<div class="add">

<a NAME="E1:26_1_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a>  <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font> #)
 
<b>by </b><i><a class="ref" href="lattice2.html#D2">LATTICE2:def 2</a></i>;<br/>
<a NAME="E2:26_1_1"/>
 <a href="lattice3.html#K2">LattRel</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lattice3.html#K2">LattRel</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K6">~</a> 
 
<b>by </b><i><a class="ref" href="lattice3.html#T20">LATTICE3:20</a></i>;<br/>
<a NAME="E3:26_1_1"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="lattice3.html#K2">LattRel</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> <a href="lattice2.html#K1">.:</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattice3.html#K2">LattRel</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K6">~</a> </span>)</span> <a href="lattice3.html#K6">~</a> 
 
<b>by </b><i><a class="ref" href="lattice3.html#T20">LATTICE3:20</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_8.html#D6">VECTSP_8:def 6</a><br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="conlat_2.html#E1:26_1_1"><i><font color="Green">E16</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E5:26_1_1"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R4">is_less_than</a>  <a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R4">is_less_than</a> <font color="Olive">b<sub>1</sub></font> holds <br/> <a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<b>by </b><i><a class="ref" href="lattice3.html#D21">LATTICE3:def 21</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> <b>by </b><i><a class="txt" href="conlat_2.html#E1:26_1_1"><i><font color="Green">E16</font></i></a></i>;<br/>
<a NAME="E7:26_1_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D16">LATTICE3:def 16</a><br/>

<b>assume </b><a NAME="E1:26_1_1_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="conlat_2.html#E1:26_1_1"><i><font color="Green">E16</font></i></a></i>;<br/>
<a NAME="E3:26_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#R3">[=</a>  <a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E5:26_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conlat_2.html#E1:26_1_1_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="lattice3.html#D17">LATTICE3:def 17</a></i>;<br/>
<a NAME="E4:26_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a>  <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K4">%</a> 
 
<b>by </b><i><a class="ref" href="lattice3.html#T7">LATTICE3:7</a></i>;<br/>
<a NAME="E5:26_1_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K4">%</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E6:26_1_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K4">%</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K6">~</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/>
<a NAME="E7:26_1_1_1"/><b>then </b><i><font color="Green">E21</font></i>: 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K4">%</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T20">LATTICE3:20</a></i>;<br/>
<a NAME="E8:26_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K4">%</a>  <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K4">%</a> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E7:26_1_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/>
<b>hence </b><a NAME="E9:26_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#R1">[=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="lattice3.html#T7">LATTICE3:7</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:26_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>5</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span>;<br/>

<b>assume </b><a NAME="E1:26_1_1_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="conlat_2.html#E1:26_1_1"><i><font color="Green">E16</font></i></a></i>;<br/>
<a NAME="E3:26_1_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R4">is_less_than</a> <font color="Maroon">c<sub>7</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D17">LATTICE3:def 17</a><br/>

<b>assume </b><a NAME="E1:26_1_1_2_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> <b>by </b><i><a class="txt" href="conlat_2.html#E1:26_1_1"><i><font color="Green">E16</font></i></a></i>;<br/>
<a NAME="E3:26_1_1_2_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E1:26_1_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conlat_2.html#E1:26_1_1_2_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="lattice3.html#D16">LATTICE3:def 16</a></i>;<br/>
<a NAME="E4:26_1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K4">%</a>  <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>9</sub></font> <a href="lattice3.html#K4">%</a> 
 
<b>by </b><i><a class="ref" href="lattice3.html#T7">LATTICE3:7</a></i>;<br/>
<a NAME="E5:26_1_1_2_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E6:26_1_1_2_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span></span>)</span> <a href="relset_1.html#K6">~</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/>
<a NAME="E7:26_1_1_2_1"/><b>then </b><i><font color="Green">E22</font></i>: 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> <a href="lattice2.html#K1">.:</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T20">LATTICE3:20</a></i>;<br/>
<a NAME="E8:26_1_1_2_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="lattice3.html#K4">%</a>  <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E3:26_1_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conlat_2.html#E7:26_1_1_2_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/>
<b>hence </b><a NAME="E9:26_1_1_2_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="lattices.html#R1">[=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="lattice3.html#T7">LATTICE3:7</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:26_1_1_2"/><b>then </b>
 <a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="lattice3.html#D21">LATTICE3:def 21</a></i>;<br/>
<a NAME="E5:26_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K4">%</a>  <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a> 
 
<b>by </b><i><a class="ref" href="lattice3.html#T7">LATTICE3:7</a></i>;<br/>
<a NAME="E6:26_1_1_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K4">%</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E7:26_1_1_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K4">%</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K6">~</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/>
<a NAME="E8:26_1_1_2"/><b>then </b><i><font color="Green">E21</font></i>: 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattice3.html#K15">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K4">%</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T20">LATTICE3:20</a></i>;<br/>
<a NAME="E9:26_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K4">%</a>  <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K4">%</a> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E8:26_1_1_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/>
<b>hence </b><a NAME="E10:26_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="lattice3.html#T7">LATTICE3:7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E9:26_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> holds <br/>(  not <font color="Olive">b<sub>2</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#R1">[=</a> <font color="Olive">b<sub>1</sub></font> ) ) )
 <b>by </b><i><a class="txt" href="conlat_2.html#E7:26_1_1"><i><font color="Green">E19</font></i></a></i>;<br/>


</div>
