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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>assume </b><a NAME="E1:37"/>
for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> <br/>for <font color="Olive">b<sub>2</sub></font> being <a href="relat_1.html#V2">V7</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Olive">b<sub>1</sub></font><br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="waybel_5.html#NM2">DoubleIndexedSet</a> of <font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> st ( for <font color="Olive">b<sub>4</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> holds  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="waybel_5.html#K1" target="_self">.</a> <font color="Olive">b<sub>4</sub></font></span>)</span> is <a href="waybel_0.html#V1">directed</a> ) holds <br/> <a href="yellow_2.html#NK7" target="_self">Inf</a>  <a href="hidden.html#R1">=</a>  <a href="yellow_2.html#NK6" target="_self">Sup</a> 
 ;<br/>

<a NAME="E2:37"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K2">the_universe_of</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>for <font color="Olive">b<sub>2</sub></font> being <a href="relat_1.html#V2">V7</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Olive">b<sub>1</sub></font> st ( for <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> holds <font color="Olive">b<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K2">the_universe_of</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> ) holds <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="waybel_5.html#NM2">DoubleIndexedSet</a> of <font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> st ( for <font color="Olive">b<sub>4</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> holds  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="waybel_5.html#K1" target="_self">.</a> <font color="Olive">b<sub>4</sub></font></span>)</span> is <a href="waybel_0.html#V1">directed</a> ) holds <br/> <a href="yellow_2.html#NK7" target="_self">Inf</a>  <a href="hidden.html#R1">=</a>  <a href="yellow_2.html#NK6" target="_self">Sup</a> 
 
;<br/>
<b>hence </b><a NAME="E3:37"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_3.html#V3">continuous</a>
 <b>by </b><i><a class="ref" href="waybel_5.html#T18" target="_self">Th18</a></i>;<br/>


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