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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A1</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A2</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<br/>





<a NAME="E1:12"/><i><font color="Green">E25</font></i>: 
<span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">A1</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">A2</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">A1</font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">A2</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:12"/>
<span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">A2</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">A1</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">A2</font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">A1</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:12"/><b>then </b><i><font color="Green">E26</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">A1</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">A2</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">A2</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">A1</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">A1</font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">A2</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">A2</font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">A1</font></span>)</span></span>)</span>
 
<b>by </b><i>, <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">A1</font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">A2</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">A2</font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">A1</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">A1</font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">A2</font></span>)</span> <a href="setlim_2.html#K2" target="_self">(\/)</a> <span class="p2">(<span class="default"><font color="Maroon">A2</font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">A1</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="prob_1.html#K2">Union</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="setlim_2.html#K4" target="_self">(\+\)</a> <font color="Maroon">A2</font></span>)</span>
<b>by </b><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">A1</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">A2</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">A1</font> <a href="setlim_2.html#K4" target="_self">(\+\)</a> <font color="Maroon">A2</font></span>)</span>
 <b>by </b><i/>;<br/>


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