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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:4_1_1_1"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E2:4_1_1_1"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>5</sub></font> <b>by </b><i><a class="txt" href="sf_mastr.html#E2:4_1_1_1"><i><font color="Green">E3</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>5</sub></font>, <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">c<sub>2</sub></font> ;<br/><a NAME="E6:4_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/><b>hence </b><a NAME="E7:4_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:4_1_1"/>
 <a href="card_3.html#K3">Union</a> <font color="Maroon">c<sub>3</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="card_4.html#T63">CARD_4:63</a></i>;<br/>


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