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<b>let </b><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">T1</font> being <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">L1</font><br/> for <font color="Olive" title="b2">T2</font> being <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="c2">L2</font><br/> for <font color="Olive" title="b3">h</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font><br/> for <font color="Olive" title="b4">H</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">T1</font>,<font color="Olive" title="b2">T2</font>  st <font color="Olive" title="b3">h</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">H</font> &amp; <font color="Olive" title="b3">h</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> holds <br/><font color="Olive" title="b4">H</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a></span><br/><b>let </b><font color="Maroon" title="c3">T1</font> be  <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">L1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">T2</font> being <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="c2">L2</font><br/> for <font color="Olive" title="b2">h</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font><br/> for <font color="Olive" title="b3">H</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">T1</font>,<font color="Olive" title="b1">T2</font>  st <font color="Olive" title="b2">h</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">H</font> &amp; <font color="Olive" title="b2">h</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> holds <br/><font color="Olive" title="b3">H</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a></span><br/><b>let </b><font color="Maroon" title="c4">T2</font> be  <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="c2">L2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">h</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font><br/> for <font color="Olive" title="b2">H</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">T1</font>,<font color="Maroon" title="c4">T2</font>  st <font color="Olive" title="b1">h</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b2">H</font> &amp; <font color="Olive" title="b1">h</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> holds <br/><font color="Olive" title="b2">H</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a></span><br/><b>let </b><font color="Maroon" title="c5">h</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">H</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">T1</font>,<font color="Maroon" title="c4">T2</font>  st <font color="Maroon" title="c5">h</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">H</font> &amp; <font color="Maroon" title="c5">h</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> holds <br/><font color="Olive" title="b1">H</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a></span><br/><b>let </b><font color="Maroon" title="c6">H</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">T1</font>,<font color="Maroon" title="c4">T2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">h</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">H</font> &amp; <font color="Maroon" title="c5">h</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> implies <font color="Maroon" title="c6">H</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> )</span><br/>









<b>assume </b><b>that </b><br/><a NAME="E1:8"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c5">h</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">H</font>
 <b>and </b><br/><a NAME="E2:8"/><i><font color="Green" title="E5">A2</font></i>: 
<font color="Maroon" title="c5">h</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">H</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a></span><br/>

<a NAME="E3:8"/><i><font color="Green" title="E6">A3</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="c1">L1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L1</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="c3">T1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">T1</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/>
<a NAME="E4:8"/><i><font color="Green" title="E7">A4</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">L2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L2</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="c4">T2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">T2</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/>
<a NAME="E5:8"/><i><font color="Green" title="E8">A5</font></i>: 
<font color="Maroon" title="c5">h</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="#E2:8"><i><font color="Green" title="E5">A2</font></i></a></i>;<br/>
<a NAME="E6:8"/><i><font color="Green" title="E9">A6</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">L2</font>
 
<b>by </b><i><a class="txt" href="#E2:8"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c1">L1</font><b> such that </b><br/><a NAME="E8:8"/><i><font color="Green" title="E10">A7</font></i>: 
<font color="Maroon" title="c7">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">h</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> 
 ;<br/>
<a NAME="E9:8"/>
<font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 
<b>by </b><i><a class="txt" href="#E5:8"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="#E6:8"><i><font color="Green" title="E9">A6</font></i></a>, <a class="txt" href="#E8:8"><i><font color="Green" title="E10">A7</font></i></a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>;<br/>
<a NAME="E10:8"/><b>then </b><i><font color="Green" title="E11">A8</font></i>: 
<font color="Maroon" title="c7">g</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 
<b>by </b><i><a class="txt" href="#E2:8"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="waybel_0.html#T68" title="WAYBEL_0:th.68">WAYBEL_0:68</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">h1</font> = <font color="Maroon" title="c5">h</font> as  <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font> <b>by </b><i><a class="txt" href="#E2:8"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="waybel13.html#T20" title="WAYBEL13:th.20">WAYBEL13:20</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">h2</font> = <font color="Maroon" title="c5">h</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  as  <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c1">L1</font> <b>by </b><i><a class="txt" href="#E8:8"><i><font color="Green" title="E10">A7</font></i></a>, <a class="txt" href="#E10:8"><i><font color="Green" title="E11">A8</font></i></a>, <a class="ref" href="waybel13.html#T20" title="WAYBEL13:th.20">WAYBEL13:20</a></i>;<br/>
<a NAME="E13:8"/><i><font color="Green" title="E12">A9</font></i>: 
<font color="Maroon" title="c8">h1</font> is <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>
 
;<br/>
<a NAME="E14:8"/><i><font color="Green" title="E13">A10</font></i>: 
<font color="Maroon" title="c9">h2</font> is <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>
 
;<br/>
<b>reconsider </b><font color="Maroon" title="c10">H'</font> = <font color="Maroon" title="c5">h</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c4">T2</font>,<font color="Maroon" title="c3">T1</font> <b>by </b><i><a class="txt" href="#E3:8"><i><font color="Green" title="E6">A3</font></i></a>, <a class="txt" href="#E4:8"><i><font color="Green" title="E7">A4</font></i></a></i>;<br/>
<a NAME="E16:8"/>
<font color="Maroon" title="c6">H</font> is <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="#E1:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E3:8"><i><font color="Green" title="E6">A3</font></i></a>, <a class="txt" href="#E4:8"><i><font color="Green" title="E7">A4</font></i></a>, <a class="txt" href="#E13:8"><i><font color="Green" title="E12">A9</font></i></a>, <a class="ref" href="waybel21.html#T6" title="WAYBEL21:th.6">WAYBEL21:6</a></i>;<br/>
<a NAME="E17:8"/><b>then </b><i><font color="Green" title="E14">A11</font></i>: 
<font color="Maroon" title="c6">H</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 
;<br/>
<a NAME="E18:8"/>
<font color="Maroon" title="c10">H'</font> is <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="#E3:8"><i><font color="Green" title="E6">A3</font></i></a>, <a class="txt" href="#E4:8"><i><font color="Green" title="E7">A4</font></i></a>, <a class="txt" href="#E14:8"><i><font color="Green" title="E13">A10</font></i></a>, <a class="ref" href="waybel21.html#T6" title="WAYBEL21:th.6">WAYBEL21:6</a></i>;<br/>
<a NAME="E19:8"/><b>then </b><i><font color="Green" title="E15">A12</font></i>: 
<font color="Maroon" title="c10">H'</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 
;<br/>
<a NAME="E20:8"/><i><font color="Green" title="E16">A13</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c3">T1</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E21:8"/><i><font color="Green" title="E17">A14</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c4">T2</font>
 
<b>by </b><i><a class="txt" href="#E1:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E2:8"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="#E4:8"><i><font color="Green" title="E7">A4</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E22:8"/><i><font color="Green" title="E18">A15</font></i>: 
<font color="Maroon" title="c6">H</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="#E1:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E2:8"><i><font color="Green" title="E5">A2</font></i></a></i>;<br/>
<i><font color="Green" title="E19">A16</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> = 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">T2</font>
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
<br/>.= 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c10">H'</font>
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
;<br/>
<a NAME="E24:8"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c10">H'</font> holds <br/><font color="Maroon" title="c10">H'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c10">H'</font> implies <font color="Maroon" title="c10">H'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> )</span><br/>

<b>assume </b><a NAME="E1:8_2"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c10">H'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">H'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span><br/>

<b>thus </b><font color="Maroon" title="c10">H'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
<b>by </b><i><a class="txt" href="#E5:8"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="#E6:8"><i><font color="Green" title="E9">A6</font></i></a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
<b>by </b><i><a class="txt" href="#E1:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E5:8"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="#E21:8"><i><font color="Green" title="E17">A14</font></i></a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E25:8"/><b>then </b>
<font color="Maroon" title="c6">H</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c10">H'</font>
 
<b>by </b><i><a class="txt" href="#E23:8"><i><font color="Green" title="E19">A16</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>
<b>hence </b><a NAME="E26:8"/>
<font color="Maroon" title="c6">H</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>
 <b>by </b><i><a class="txt" href="#E17:8"><i><font color="Green" title="E14">A11</font></i></a>, <a class="txt" href="#E19:8"><i><font color="Green" title="E15">A12</font></i></a>, <a class="txt" href="#E20:8"><i><font color="Green" title="E16">A13</font></i></a>, <a class="txt" href="#E21:8"><i><font color="Green" title="E17">A14</font></i></a>, <a class="txt" href="#E22:8"><i><font color="Green" title="E18">A15</font></i></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
