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<b>let </b><font color="Maroon" title="c1">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">H</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c2">S</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:49"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 <b>and </b><br/><a NAME="E2:49"/><i><font color="Green" title="E24">A2</font></i>: 
<font color="Maroon" title="c4">H</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font>;<br/>

<b>assume </b><a NAME="E3:49"/><i><font color="Green" title="E25">A3</font></i>: 
<font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3" title="FUNCT_3:func.3">"</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Maroon" title="c4">H</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c6">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D1" target="_self" title="TOPS_2:def.1">TOPS_2:def 1</a><br/>

<b>assume </b><a NAME="E4:49"/>
<font color="Maroon" title="c6">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c7">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:49"/><i><font color="Green" title="E26">A4</font></i>: 
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3" title="FUNCT_3:func.3">"</a> <font color="Maroon" title="c3">f</font></span>)</span>
 <b>and </b><br/><a NAME="E7:49"/><i><font color="Green" title="E27">A5</font></i>: 
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">H</font>
 <b>and </b><br/><a NAME="E8:49"/><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c6">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3" title="FUNCT_3:func.3">"</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font>
 <b>by </b><i><a class="txt" href="tops_2.html#E3:49"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">Y</font> = <font color="Maroon" title="c7">y</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">S</font> <b>by </b><i><a class="txt" href="tops_2.html#E7:49"><i><font color="Green" title="E27">A5</font></i></a></i>;<br/>
<a NAME="E10:49"/><i><font color="Green" title="E29">A7</font></i>: 
<font color="Maroon" title="c6">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c8">Y</font>
 
<b>by </b><i><a class="txt" href="tops_2.html#E6:49"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="tops_2.html#E8:49"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="funct_3.html#T24" title="FUNCT_3:th.24">FUNCT_3:24</a></i>;<br/>
<a NAME="E11:49"/>
<font color="Maroon" title="c8">Y</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="txt" href="tops_2.html#E2:49"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="tops_2.html#E7:49"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="tops_2.html#D1" target="_self" title="TOPS_2:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E12:49"/>
<font color="Maroon" title="c6">X</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="txt" href="tops_2.html#E1:49"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="tops_2.html#E10:49"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="tops_2.html#T55" target="_self" title="TOPS_2:th.55">Th55</a></i>;<br/>


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