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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:80_1_1_1"/><i><font color="Green" title="E53">A1</font></i>: 
<font color="Maroon" title="c5">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="c4">f</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c6">A</font> = <font color="Maroon" title="c2">A</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/><b>reconsider </b><font color="Maroon" title="c7">x'</font> = <font color="Maroon" title="c5">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">A</font> <b>by </b><i><a class="txt" href="card_4.html#E1:80_1_1_1"><i><font color="Green" title="E53">A1</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">f'</font> = <font color="Maroon" title="c4">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c6">A</font>, <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c3">B</font> ;<br/><a NAME="E5:80_1_1_1"/>
<font color="Maroon" title="c8">f'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x'</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ;<br/><b>hence </b><a NAME="E6:80_1_1_1"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:80_1_1"/>
 <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Maroon" title="c4">f</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="ref" href="card_4.html#T63" target="_self" title="CARD_4:th.63">Th63</a></i>;<br/>


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