<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> 1</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">T</font> =  <a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">CT</font> =  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="16_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span><br/>  for <font color="Olive" title="b2">U</font> being   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span>  st <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">U</font> holds <br/> ex <font color="Olive" title="b3">W</font> being   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">W</font> &amp; <font color="Olive" title="b3">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">U</font> &amp;  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Olive" title="b3">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">U</font> being   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span>  st <font color="Maroon" title="c4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">U</font> holds <br/> ex <font color="Olive" title="b2">W</font> being   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> st <br/>( <font color="Maroon" title="c4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">W</font> &amp; <font color="Olive" title="b2">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">U</font> &amp;  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Olive" title="b2">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">U</font> be   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">U</font> implies  ex <font color="Olive" title="b1">W</font> being   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> st <br/>( <font color="Maroon" title="c4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp; <font color="Olive" title="b1">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">U</font> &amp;  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Olive" title="b1">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ) )</span><br/><span class="kw">assume </span><a NAME="E1:16_1"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">U</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">W</font> being   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> st <br/>( <font color="Maroon" title="c4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp; <font color="Olive" title="b1">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">U</font> &amp;  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Olive" title="b1">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> )</span><br/><span class="kw">take </span><font color="Maroon" title="c6">W</font> = <font color="Maroon" title="c5">U</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">W</font> &amp; <font color="Maroon" title="c6">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">U</font> &amp;  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Maroon" title="c6">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> )</span><br/><a NAME="E2:16_1"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#D5" onmouseover="rs('pre_topc/D5')" onmouseout="rh()">PRE_TOPC:def 5</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">W9</font> = <font color="Maroon" title="c5">U</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> ;<br/><a NAME="E4:16_1"/>
<font color="Maroon" title="c7">W9</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#D2" onmouseover="rs('pre_topc/D2')" onmouseout="rh()">PRE_TOPC:def 2</a></span>;<br/><a NAME="E5:16_1"/><span class="kw">then </span>
( <font color="Maroon" title="c7">W9</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Maroon" title="c7">W9</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#D2" onmouseover="rs('pre_topc/D2')" onmouseout="rh()">PRE_TOPC:def 2</a>, <a class="ref" href="tops_1.html#T3" onmouseover="rs('tops_1/T3')" onmouseout="rh()">TOPS_1:3</a></span>;<br/><a NAME="E6:16_1"/><span class="kw">then </span>
 <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Maroon" title="c7">W9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topgen_1.html#T14" onmouseover="rs('topgen_1/T14')" onmouseout="rh()">TOPGEN_1:14</a></span>;<br/><a NAME="E7:16_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<span class="p1">(<span class="default"><a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Maroon" title="c7">W9</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E8:16_1"/>
<font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">W</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="xboole_1.html#T28" onmouseover="rs('xboole_1/T28')" onmouseout="rh()">XBOOLE_1:28</a></span>;<br/><a NAME="E9:16_1"/><span class="kw">then </span>
 <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Maroon" title="c6">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:16_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="topdim_1.html#T1" target="_self" onmouseover="rs('topdim_1/T1')" onmouseout="rh()">Th1</a></span>;<br/><a NAME="E10:16_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A4</font></span>: 
 <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Maroon" title="c6">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span>
 ;<br/><a NAME="E11:16_1"/>
<span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p3">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topdim_1.html#D1" target="_self" onmouseover="rs('topdim_1/D1')" onmouseout="rh()">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E12:16_1"/>
( <font color="Maroon" title="c4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">W</font> &amp; <font color="Maroon" title="c6">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">U</font> &amp;  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Maroon" title="c6">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E10:16_1"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E2:16"/><span class="kw">then </span>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topdim_1.html#D1" target="_self" onmouseover="rs('topdim_1/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:16"/>
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="topdim_1.html#K1" title="TOPDIM_1:func.1">Seq_of_ind</a> <span class="p2">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="prob_1.html#K13" title="PROB_1:func.13">.</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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