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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_3.html#V3">continuous</a> <a href="waybel_0.html#NM7">sup-Semilattice</a>;<br/>

<b>assume </b><a NAME="E1:24"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="group_1.html#V6">finite</a>
 ;<br/>

<a NAME="E2:24"/><b>then </b><i><font color="Green">E19</font></i>: 
not the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="group_1.html#D14">GROUP_1:def 14</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="waybel23.html#V6">with_bottom</a>  <a href="waybel23.html#M1">CLbasis</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E3:24"/><i><font color="Green">E20</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="waybel23.html#K3">supMap</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K7">Ids</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel23.html#T51">WAYBEL23:51</a></i>;<br/>
<a NAME="E4:24"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="waybel23.html#K3">supMap</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="waybel23.html#T65">WAYBEL23:65</a></i>;<br/>
<a NAME="E5:24"/><b>then </b>
 <a href="card_1.html#K1">Card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="ordinal1.html#R1">c=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel31.html#E3:24"><i><font color="Green">E20</font></i></a>, <a class="ref" href="card_1.html#T28">CARD_1:28</a></i>;<br/>
<a NAME="E6:24"/><b>then </b>
not  <a href="waybel_0.html#K7">Ids</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="txt" href="waybel31.html#E2:24"><i><font color="Green">E19</font></i></a>, <a class="ref" href="card_2.html#T68">CARD_2:68</a></i>;<br/>
<a NAME="E7:24"/><b>then </b>
not  <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>2</sub></font> is <a href="group_1.html#V6">finite</a>
 
<b>by </b><i><a class="ref" href="waybel31.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E8:24"/><b>then </b>
not the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="group_1.html#D14">GROUP_1:def 14</a></i>;<br/>
<b>hence </b><a NAME="E9:24"/>
not <font color="Maroon">c<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>


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