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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: WAYBEL31:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L1</font> being   <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>  st <font color="Olive" title="b1">L1</font> is  <a href="struct_0.html#NV10" title="STRUCT_0:NV.10">infinite</a>  holds <br/> for <font color="Olive" title="b2">B1</font> being   <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="Olive" title="b1">L1</font> holds   <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="waybel31.html#K2" title="WAYBEL31:func.2">Way_Up</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">A</font>)</span>)</span> where <font color="Olive" title="b3">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L1</font>, <font color="Olive" title="b4">A</font> is   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L1</font> : ( <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">B1</font> &amp; <font color="Olive" title="b4">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">B1</font> ) </span> } </span>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b2">B1</font></div></div>
