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<b>let </b><font color="Maroon" title="c1">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</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="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> implies <font color="Maroon" title="c1">T</font> is <a href="topgen_2.html#V1" title="TOPGEN_2:attr.1">finite-weight</a> )</span><br/>

<b>consider </b><font color="Maroon" title="c2">B</font> being    <a href="cantor_1.html#M1" title="CANTOR_1:mode.1">Basis</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E2:22_1_1"/><i><font color="Green" title="E14">A1</font></i>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="ref" href="waybel23.html#T75" title="WAYBEL23:th.75">WAYBEL23:75</a></i>;<br/>
<b>assume </b><a NAME="E3:22_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D11" title="STRUCT_0:def.11">STRUCT_0:def 11</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="topgen_2.html#V1" title="TOPGEN_2:attr.1">finite-weight</a></span><br/>

<a NAME="E4:22_1_1"/><b>then </b>
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
;<br/>
<a NAME="E5:22_1_1"/><b>then </b>
<font color="Maroon" title="c2">B</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
;<br/>
<b>hence </b><a NAME="E6:22_1_1"/>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="txt" href="#E2:22_1_1"><i><font color="Green" title="E14">A1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="topgen_2.html#D4" target="_self" title="TOPGEN_2:def.4">TOPGEN_2:def 4</a> <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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