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<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5">EqRelLatt</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> is   <a href="msualg_4.html#NM5">MSCongruence</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <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> ) </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:16_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5">EqRelLatt</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> is   <a href="msualg_4.html#NM5">MSCongruence</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <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> ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5">EqRelLatt</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:16_1_1_1"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> is   <a href="msualg_4.html#NM5">MSCongruence</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R4">is_less_than</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><b>thus </b><a NAME="E4:16_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K6">CongrLatt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="msualg_8.html#E3:16_1_1_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="msualg_5.html#D6">MSUALG_5:def 6</a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5">EqRelLatt</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> is   <a href="msualg_4.html#NM5">MSCongruence</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <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> ) </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K6">CongrLatt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E3:16_1_1"/>
 <a href="lattice3.html#K16">"/\"</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="msualg_5.html#K5">EqRelLatt</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> is   <a href="msualg_4.html#NM5">MSCongruence</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_8.html#T11" target="_self">Th11</a></i>;<br/>
<b>hence </b><a NAME="E4:16_1_1"/>
 <a href="lattice3.html#K16">"/\"</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5">EqRelLatt</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> is   <a href="msualg_4.html#NM5">MSCongruence</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <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> ) </span>}</span> ,<span class="p1">(<span class="default"><a href="msualg_5.html#K5">EqRelLatt</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> is   <a href="msualg_4.html#NM5">MSCongruence</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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