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<b>let </b><font color="Maroon" title="c1">T</font> be  <a href="compts_1.html#NV4" title="COMPTS_1:NV.4">Hausdorff</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"> for <font color="Olive" title="b1">N</font> being <a href="yellow_6.html#V3" title="YELLOW_6:attr.3">convergent</a> <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">T</font><br/> for <font color="Olive" title="b2">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b2">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a>  is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> holds <br/><font color="Olive" title="b2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K12" title="YELLOW_6:func.12">lim</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="waybel_9.html#K1" title="WAYBEL_9:func.1">"/\"</a> <font color="Olive" title="b1">N</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">N</font> be  <a href="yellow_6.html#V3" title="YELLOW_6:attr.3">convergent</a> <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a>  is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> holds <br/><font color="Olive" title="b1">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K12" title="YELLOW_6:func.12">lim</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="waybel_9.html#K1" title="WAYBEL_9:func.1">"/\"</a> <font color="Maroon" title="c2">N</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a>  is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> implies <font color="Maroon" title="c3">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K12" title="YELLOW_6:func.12">lim</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_9.html#K1" title="WAYBEL_9:func.1">"/\"</a> <font color="Maroon" title="c2">N</font></span>)</span> )</span><br/>





<b>assume </b><a NAME="E1:78"/><i><font color="Green" title="E31">A1</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a>  is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K12" title="YELLOW_6:func.12">lim</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_9.html#K1" title="WAYBEL_9:func.1">"/\"</a> <font color="Maroon" title="c2">N</font></span>)</span></span><br/>

<a NAME="E2:78"/>
<font color="Maroon" title="c3">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K12" title="YELLOW_6:func.12">lim</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K12" title="YELLOW_6:func.12">lim</a> <font color="Maroon" title="c2">N</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_1.html#D18" title="WAYBEL_1:def.18">WAYBEL_1:def 18</a></i>;<br/>
<a NAME="E3:78"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K12" title="YELLOW_6:func.12">lim</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c2">N</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:78"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="waybel_9.html#T25" target="_self" title="WAYBEL_9:th.25">Th25</a></i>;<br/>
<b>hence </b><a NAME="E4:78"/>
<font color="Maroon" title="c3">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K12" title="YELLOW_6:func.12">lim</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_9.html#K1" title="WAYBEL_9:func.1">"/\"</a> <font color="Maroon" title="c2">N</font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_9.html#T18" target="_self" title="WAYBEL_9:th.18">Th18</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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