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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <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">A</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">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a>  iff ( <font color="Olive" title="b1">A</font> is  <a href="isomichi.html#V1" title="ISOMICHI:attr.1">supercondensed</a>  &amp; <font color="Olive" title="b1">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <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">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a>  iff ( <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#V1" title="ISOMICHI:attr.1">supercondensed</a>  &amp; <font color="Maroon" title="c2">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  ) )</span><br/>



<span class="kw">thus </span><a NAME="E1:32"/>
( <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a>  implies ( <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#V1" title="ISOMICHI:attr.1">supercondensed</a>  &amp; <font color="Maroon" title="c2">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</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">A</font> is  <a href="isomichi.html#V1" title="ISOMICHI:attr.1">supercondensed</a>  &amp; <font color="Maroon" title="c2">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  implies <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:32_1"/>
<font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</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">A</font> is  <a href="isomichi.html#V1" title="ISOMICHI:attr.1">supercondensed</a>  &amp; <font color="Maroon" title="c2">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  )</span><br/>

<a NAME="E2:32_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A1</font></span>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tops_1.html#D8" title="TOPS_1:def.8">TOPS_1:def 8</a></span>;<br/>
<a NAME="E3:32_1"/><span class="kw">then </span>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E4:32_1"/>
( <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#V1" title="ISOMICHI:attr.1">supercondensed</a>  &amp; <font color="Maroon" title="c2">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32_1"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="isomichi.html#D1" target="_self" title="ISOMICHI:def.1">Def1</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/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:32"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#V1" title="ISOMICHI:attr.1">supercondensed</a> 
 <span class="kw">and </span><br/><a NAME="E3:32"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
<font color="Maroon" title="c2">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</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">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a> </span><br/>

<a NAME="E4:32"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="isomichi.html#D1" target="_self" title="ISOMICHI:def.1">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:32"/>
<font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:32"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="tops_1.html#T23" title="TOPS_1:th.23">TOPS_1:23</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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