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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">Y</font> be  <a href="waybel25.html#V1">monotone-convergence</a> <a href="t_0topsp.html#NM1">T_0-TopSpace</a>;<br/>



<a NAME="E1:16"/><i><font color="Green">E45</font></i>: 
 <a href="waybel24.html#K3">ContMaps</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="waybel25.html#K1">Omega</a> <font color="Maroon">Y</font></span>)</span> is  <a href="yellow_0.html#V4">full</a> <a href="waybel_0.html#V4">directed-sups-inheriting</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1">Omega</a> <font color="Maroon">Y</font></span>)</span> <a href="yellow_1.html#K6">|^</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="waybel24.html#D3">WAYBEL24:def 3</a>, <a class="ref" href="waybel25.html#T43">WAYBEL25:43</a></i>;<br/>
<b>thus </b><a NAME="E2:16"/>
 <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> is <a href="waybel_0.html#V24">up-complete</a>
 <b>by </b><i>, <a class="ref" href="yellow16.html#T5">YELLOW16:5</a></i>;<br/>


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