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<b>let </b><font color="Maroon" title="c1">T</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a> <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> iff  <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">T</font> )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">T</font> implies <font color="Maroon" title="c1">T</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> )</span>
<div class="add"><b>assume </b><a NAME="E1:98_1"/>
<font color="Maroon" title="c1">T</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">T</font></span><br/><b>then reconsider </b><font color="Maroon" title="c2">L</font> = <font color="Maroon" title="c1">T</font> as  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a> <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a> ;<br/><a NAME="E3:98_1"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">T</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_6.html#K14" title="YELLOW_6:func.14">ConvergenceSpace</a> <span class="p1">(<span class="default"><a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel11.html#T32" target="_self" title="WAYBEL11:th.32">Th32</a></i>;<br/><b>hence </b> <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c1">T</font> = 
 <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K14" title="YELLOW_6:func.14">ConvergenceSpace</a> <span class="p2">(<span class="default"><a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="waybel11.html#E57"><i><font color="Green" title="E48">Lm8</font></i></a></i>
<br/>.= 
 <a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">T</font>
<b>by </b><i><a class="ref" href="yellow_6.html#T53" title="YELLOW_6:th.53">YELLOW_6:53</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:98"/>
(  <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">T</font> implies <font color="Maroon" title="c1">T</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> )
 <b>by </b><i><a class="ref" href="waybel11.html#T39" target="_self" title="WAYBEL11:th.39">Th39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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