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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:21"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:21"/>
( <font color="Maroon">c<sub>3</sub></font>, <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>3</sub></font> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <font color="Maroon">c<sub>4</sub></font>, <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>4</sub></font> <a href="wellord2.html#R2">are_equipotent</a>  &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 
<b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a></i>;<br/>
<a NAME="E3:21"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">H<sub>4</sub></font>( <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>3</sub></font>, <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>)
 
<b>by </b><i><a class="txt" href="card_2.html#E1:21"><i><font color="Green">E18</font></i></a>, <a class="ref" href="card_2.html#T23" target="_self">Th23</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="card_2.html#K1" target="_self">+`</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ordinal2.html#K10">+^</a> <span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="card_2.html#E1:21"><i><font color="Green">E18</font></i></a>, <a class="txt" href="card_2.html#E3:21"><i><font color="Green">E19</font></i></a>, <a class="txt" href="card_2.html#E8"><i><font color="Green">Lemma3</font></i></a></i>
;<br/>


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