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<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K5">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font></span><a href="domain_1.html#K5">]</a></span> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>, B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> : <font color="Maroon">c<sub>3</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">b<sub>4</sub></font> </span>}</span> ;<br/>
<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:42_1_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>5</sub></font>,<span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K5">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font></span><a href="domain_1.html#K5">]</a></span> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>, B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> : <font color="Maroon">c<sub>3</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">b<sub>4</sub></font> </span>}</span>  <a href="tarski.html#R2">are_equipotent</a> 
 <b>and </b><br/><a NAME="E2:42_1_2"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K5">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font></span><a href="domain_1.html#K5">]</a></span> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>, B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> : <font color="Maroon">c<sub>3</sub></font> <a href="lattice5.html#K4" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">b<sub>4</sub></font> </span>}</span>  <a href="tarski.html#R2">are_equipotent</a> 
 ;<br/>

<a NAME="E3:42_1_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R2">are_equipotent</a> 
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:42_1_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="lattice5.html#E2:42_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="wellord2.html#T22">WELLORD2:22</a></i>;<br/>
<b>hence </b><a NAME="E4:42_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="card_1.html#T8">CARD_1:8</a></i>;<br/>


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