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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:12"/><i><font color="Green">E16</font></i>: 
<span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="prob_1.html#K2">Union</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="setlim_2.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E2:12"/>
<span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="prob_1.html#K2">Union</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="setlim_2.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E3:12"/><b>then </b><i><font color="Green">E17</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="setlim_2.html#E1:12"><i><font color="Green">E16</font></i></a>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
 <a href="prob_1.html#K2">Union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="setlim_2.html#K2" target="_self">(\/)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T9" target="_self">Th9</a></i>
<br/>.= 
 <a href="prob_1.html#K2">Union</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K4" target="_self">(\+\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T3" target="_self">Th3</a></i>
;<br/>
<b>hence </b><a NAME="E5:12"/>
<span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K5">\+\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="prob_1.html#K2">Union</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K4" target="_self">(\+\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="setlim_2.html#E3:12"><i><font color="Green">E17</font></i></a></i>;<br/>


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