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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="waybel11.html#V4" target="_self">Scott</a> <a href="waybel_9.html#NM1">TopLattice</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:99_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_3.html#V3">continuous</a>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="lattice3.html#V3">complete</a> <a href="waybel_3.html#V3">continuous</a> <a href="waybel11.html#V4" target="_self">Scott</a> <a href="waybel_9.html#NM1">TopLattice</a> ;<br/><a NAME="E3:99_1"/>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="yellow_6.html#K14">ConvergenceSpace</a> <span class="p1">(<span class="default"><a href="waybel11.html#K2" target="_self">Scott-Convergence</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel11.html#T32" target="_self">Th32</a></i>;<br/><b>hence </b> <a href="yellow_6.html#K13">Convergence</a> <font color="Maroon">c<sub>1</sub></font> = 
 <a href="yellow_6.html#K13">Convergence</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K14">ConvergenceSpace</a> <span class="p2">(<span class="default"><a href="waybel11.html#K2" target="_self">Scott-Convergence</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="waybel11.html#E57"><i><font color="Green">Lemma48</font></i></a></i>
<br/>.= 
 <a href="waybel11.html#K2" target="_self">Scott-Convergence</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="yellow_6.html#T53">YELLOW_6:53</a></i>
;<br/><br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:99"/>
(  <a href="yellow_6.html#K13">Convergence</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K2" target="_self">Scott-Convergence</a> <font color="Maroon">c<sub>1</sub></font> implies <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="waybel11.html#T39" target="_self">Th39</a></i>;<br/>


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