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<b>let </b><font color="Maroon" title="c1">L1</font> be  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> <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>;<br/>

<b>assume </b><a NAME="E1:24"/>
not <font color="Maroon" title="c1">L1</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 ;<br/>

<a NAME="E2:24"/><b>then </b><i><font color="Green" title="E17">A1</font></i>: 
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="struct_0.html#D11" title="STRUCT_0:def.11">STRUCT_0:def 11</a></i>;<br/>
<b>let </b><font color="Maroon" title="c2">B1</font> be  <a href="waybel23.html#V6" title="WAYBEL23:attr.6">with_bottom</a>  <a href="waybel23.html#M1" title="WAYBEL23:mode.1">CLbasis</a> of <font color="Maroon" title="c1">L1</font>;<br/>

<a NAME="E3:24"/><i><font color="Green" title="E18">A2</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="waybel23.html#K3" title="WAYBEL23:func.3">supMap</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel23.html#T51" title="WAYBEL23:th.51">WAYBEL23:51</a></i>;<br/>
<a NAME="E4:24"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="waybel23.html#K3" title="WAYBEL23:func.3">supMap</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>
 
<b>by </b><i><a class="ref" href="waybel23.html#T65" title="WAYBEL23:th.65">WAYBEL23:65</a></i>;<br/>
<a NAME="E5:24"/><b>then </b>
 <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">L1</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> <span class="p1">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel31.html#E3:24"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="card_1.html#T28" title="CARD_1:th.28">CARD_1:28</a></i>;<br/>
<a NAME="E6:24"/><b>then </b>
not  <a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B1</font></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="txt" href="waybel31.html#E2:24"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="card_2.html#T68" title="CARD_2:th.68">CARD_2:68</a></i>;<br/>
<a NAME="E7:24"/><b>then </b>
not  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B1</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 
<b>by </b><i><a class="ref" href="waybel31.html#T19" target="_self" title="WAYBEL31:th.19">Th19</a></i>;<br/>
<a NAME="E8:24"/><b>then </b>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B1</font></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="struct_0.html#D11" title="STRUCT_0:def.11">STRUCT_0:def 11</a></i>;<br/>
<b>hence </b><a NAME="E9:24"/>
not <font color="Maroon" title="c2">B1</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>


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