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<span class="kw">thus </span><a NAME="E1:21_1_1"/>
( <font color="Maroon" title="c1">T</font> is  <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  implies  for <font color="Olive" title="b1">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds <br/> ( <font color="Olive" title="b1">S</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  iff <font color="Olive" title="b1">S</font> is  <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>  ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel11.html#D4" target="_self" title="WAYBEL11:def.4">Def4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds <br/> ( <font color="Olive" title="b1">S</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  iff <font color="Olive" title="b1">S</font> is  <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>  ) ) implies <font color="Maroon" title="c1">T</font> is  <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:21_1_1"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
 for <font color="Olive" title="b1">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds <br/> ( <font color="Olive" title="b1">S</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  iff <font color="Olive" title="b1">S</font> is  <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">T</font> is  <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel11.html#D4" target="_self" title="WAYBEL11:def.4">WAYBEL11:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  iff ( <font color="Maroon" title="c2">S</font> is  <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>  ) )</span><br/>

<span class="kw">thus </span><a NAME="E3:21_1_1"/>
( <font color="Maroon" title="c2">S</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  iff ( <font color="Maroon" title="c2">S</font> is  <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>  ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a></span>; <a class="txt" 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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