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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L1</font> being   <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  <a href="waybel_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>  st  <a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  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> <font color="Olive" title="b1">L1</font> holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">L1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">L1</font> be   <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  <a href="waybel_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  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> <font color="Maroon" title="c2">L1</font> implies  <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L1</font> )</span><br/>



<a NAME="E1:11"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow15.html#T28" onmouseover="rs('yellow15/T28')" onmouseout="rh()">YELLOW15:28</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:11"/>
 <a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  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> <font color="Maroon" title="c2">L1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L1</font></span><br/>

<span class="kw">hence </span><a NAME="E3:11"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="yellow_1.html#T1" onmouseover="rs('yellow_1/T1')" onmouseout="rh()">YELLOW_1:1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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