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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:72"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:72_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:72_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E4:72_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="yellow_2.html#E3:72_1"><i><font color="Green">E36</font></i></a></i>;<br/><a NAME="E6:72_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="yellow_2.html#E4:72_1"><i><font color="Green">E37</font></i></a></i>;<br/><b>hence </b><a NAME="E7:72_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="yellow_2.html#E1:72"><i><font color="Green">E35</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E3:72"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#R1">is_&lt;=_than</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/>
<a NAME="E4:72"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#K2">"/\"</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T33">YELLOW_0:33</a></i>;<br/>
<b>hence </b><a NAME="E5:72"/>
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_2.html#NK7" target="_self">Inf</a> 
 ;<br/>


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