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<b>consider </b><font color="Maroon" title="c2">T</font> being  <a href="yellow_9.html#NV1" title="YELLOW_9:NV.1">correct</a> <a href="waybel19.html#V1" title="WAYBEL19:attr.1">lower</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c1">R</font>;<br/>
<b>consider </b><font color="Maroon" title="c3">S</font> being  <a href="yellow_9.html#NV1" title="YELLOW_9:NV.1">correct</a> <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c1">R</font>;<br/>
<a NAME="E3:42_1_1"/><i><font color="Green" title="E28">A1</font></i>: 
(  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">T</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font> #) &amp;  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font> #) )
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4" title="YELLOW_9:def.4">YELLOW_9:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">RR</font> being    <a href="yellow_9.html#M3" title="YELLOW_9:mode.3">Refinement</a> of <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c2">T</font>;<br/>
<a NAME="E5:42_1_1"/><i><font color="Green" title="E29">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">RR</font> <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="c3">S</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#D6" title="YELLOW_9:def.6">YELLOW_9:def 6</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">O</font> = the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c4">RR</font> as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="txt" href="#E3:42_1_1"><i><font color="Green" title="E28">A1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">LL</font> =  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c5">O</font> #);<br/>
<a NAME="E7:42_1_1"/>
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c5">O</font> #),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c5">O</font> #) #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font> #)
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">LL</font> =  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c5">O</font> #) as    <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="ref" href="yellow_9.html#D4" title="YELLOW_9:def.4">YELLOW_9:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c7">LL</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">LL</font> is <a href="waybel19.html#V2" title="WAYBEL19:attr.2">Lawson</a> &amp; <font color="Maroon" title="c7">LL</font> is <a href="waybel_9.html#V1" title="WAYBEL_9:attr.1">strict</a> &amp; <font color="Maroon" title="c7">LL</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a> )</span><br/>

<a NAME="E9:42_1_1"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">LL</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c7">LL</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">RR</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c4">RR</font> #)
 
<b>by </b><i><a class="txt" href="#E3:42_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E5:42_1_1"><i><font color="Green" title="E29">A2</font></i></a></i>;<br/>
<a NAME="E10:42_1_1"/><b>then </b><i><font color="Green" title="E30">A3</font></i>: 
<font color="Maroon" title="c7">LL</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a>
 
<b>by </b><i><a class="ref" href="tex_2.html#T12" title="TEX_2:th.12">TEX_2:12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">A</font> = the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c3">S</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">T</font> as    <a href="cantor_1.html#M2" title="CANTOR_1:mode.2">prebasis</a> of <font color="Maroon" title="c4">RR</font> <b>by </b><i><a class="ref" href="yellow_9.html#D6" title="YELLOW_9:def.6">YELLOW_9:def 6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">A'</font> = <font color="Maroon" title="c8">A</font> as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c7">LL</font> <b>by </b><i><a class="txt" href="#E3:42_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E5:42_1_1"><i><font color="Green" title="E29">A2</font></i></a></i>;<br/>
<a NAME="E13:42_1_1"/>
 <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <font color="Maroon" title="c8">A</font> is    <a href="cantor_1.html#M1" title="CANTOR_1:mode.1">Basis</a> of <font color="Maroon" title="c4">RR</font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T23" title="YELLOW_9:th.23">YELLOW_9:23</a></i>;<br/>
<a NAME="E14:42_1_1"/><b>then </b>
 <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <font color="Maroon" title="c8">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">O</font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T22" title="YELLOW_9:th.22">YELLOW_9:22</a></i>;<br/>
<a NAME="E15:42_1_1"/><b>then </b>
 <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <font color="Maroon" title="c9">A'</font> is    <a href="cantor_1.html#M1" title="CANTOR_1:mode.1">Basis</a> of <font color="Maroon" title="c7">LL</font>
 
<b>by </b><i><a class="txt" href="#E3:42_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E5:42_1_1"><i><font color="Green" title="E29">A2</font></i></a>, <a class="txt" href="#E10:42_1_1"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="yellow_9.html#T22" title="YELLOW_9:th.22">YELLOW_9:22</a></i>;<br/>
<a NAME="E16:42_1_1"/><b>then </b>
the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c3">S</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">T</font> is    <a href="cantor_1.html#M2" title="CANTOR_1:mode.2">prebasis</a> of <font color="Maroon" title="c7">LL</font>
 
<b>by </b><i><a class="txt" href="#E10:42_1_1"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="yellow_9.html#T23" title="YELLOW_9:th.23">YELLOW_9:23</a></i>;<br/>
<a NAME="E17:42_1_1"/><b>then </b>
<font color="Maroon" title="c7">LL</font> is    <a href="yellow_9.html#M3" title="YELLOW_9:mode.3">Refinement</a> of <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="txt" href="#E3:42_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E5:42_1_1"><i><font color="Green" title="E29">A2</font></i></a>, <a class="txt" href="#E10:42_1_1"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="yellow_9.html#D6" title="YELLOW_9:def.6">YELLOW_9:def 6</a></i>;<br/>
<b>hence </b><a NAME="E18:42_1_1"/>
( <font color="Maroon" title="c7">LL</font> is <a href="waybel19.html#V2" title="WAYBEL19:attr.2">Lawson</a> &amp; <font color="Maroon" title="c7">LL</font> is <a href="waybel_9.html#V1" title="WAYBEL_9:attr.1">strict</a> &amp; <font color="Maroon" title="c7">LL</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a> )
 <b>by </b><i><a class="ref" href="waybel19.html#T29" target="_self" title="WAYBEL19:th.29">Th29</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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