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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="unialg_2.html#V2">with_const_op</a> <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K12">UnSubAlLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be  <a href="unialg_1.html#V3">strict</a>  <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:24"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<b>thus </b><a NAME="E2:24"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>4</sub></font> is    <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">c<sub>5</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:24_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:24_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="unialg_3.html#E1:24"><i><font color="Green">E15</font></i></a>, <a class="ref" href="unialg_3.html#T17" target="_self">Th17</a></i>;<br/>
<b>hence </b><a NAME="E3:24_1"/>
<font color="Maroon">c<sub>4</sub></font> is    <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="unialg_2.html#T14">UNIALG_2:14</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:24"/>
( <font color="Maroon">c<sub>4</sub></font> is    <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">c<sub>5</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:24_2"/>
<font color="Maroon">c<sub>4</sub></font> is    <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:24_2"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D8">UNIALG_2:def 8</a></i>;<br/>
<b>hence </b><a NAME="E3:24_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="unialg_3.html#E1:24"><i><font color="Green">E15</font></i></a>, <a class="ref" href="unialg_3.html#T17" target="_self">Th17</a></i>;<br/>


</div><b>end;</b></div>


</div>
