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<b>let </b><font color="Maroon" title="c1">f</font> be  <a href="cohsp_1.html#V8" title="COHSP_1:attr.8">U-continuous</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>

<b>assume </b><a NAME="E1:59"/><i><font color="Green" title="E27">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> is <a href="classes1.html#V1" title="CLASSES1:attr.1">subset-closed</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E2:59"/><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c3">C</font> =  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="classes1.html#V1" title="CLASSES1:attr.1">subset-closed</a> <a href="cohsp_1.html#V3" title="COHSP_1:attr.3">d.union-closed</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="txt" href="cohsp_1.html#E1:59"><i><font color="Green" title="E27">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">a</font> = <font color="Maroon" title="c2">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">C</font> <b>by </b><i><a class="txt" href="cohsp_1.html#E2:59"><i><font color="Green" title="E28">A2</font></i></a></i>;<br/>
<a NAME="E5:59"/>
<font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K4" title="COHSP_1:func.4">union</a> <span class="p2">(<span class="default"><a href="cohsp_1.html#K3" title="COHSP_1:func.3">Fin</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T20" target="_self" title="COHSP_1:th.20">Th20</a></i>;<br/>
<b>hence </b><a NAME="E6:59"/>
<font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p2">(<span class="default"><a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="cohsp_1.html#D11" target="_self" title="COHSP_1:def.11">Def11</a></i>;<br/>


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