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<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="classes1.html#K4">Rank</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> as   <a href="ordinal2.html#NM1">Ordinal-Sequence</a> <b>by </b><i><a class="ref" href="zf_refle.html#T11" target="_self">Th11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> as   <a href="ordinal1.html#NM2">Ordinal</a> <b>by </b><i><a class="ref" href="zf_refle.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E3:21_1_1"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K3">On</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="classes1.html#NR1" target="_self">is_Tarski-Class</a>  &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="zf_refle.html#T8" target="_self">Th8</a>, <a class="ref" href="funct_1.html#T89">FUNCT_1:89</a>, <a class="ref" href="relat_1.html#T116">RELAT_1:116</a></i>;<br/>
<a NAME="E4:21_1_1"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K4">Rank</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="classes1.html#K4">Rank</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="classes2.html#T26">CLASSES2:26</a>, <a class="ref" href="relat_1.html#T87">RELAT_1:87</a></i>;<br/>
<a NAME="E5:21_1_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>
<a NAME="E6:21_1_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="zf_refle.html#E3:21_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>
<a NAME="E7:21_1_1"/><b>then </b>
(  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="card_2.html#T3">CARD_2:3</a>, <a class="ref" href="classes2.html#T1">CLASSES2:1</a>, <a class="ref" href="relat_1.html#T146">RELAT_1:146</a></i>;<br/>
<a NAME="E8:21_1_1"/><b>then </b>
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#T22">ORDINAL1:22</a></i>;<br/>
<a NAME="E9:21_1_1"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K8">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="zf_refle.html#E3:21_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="classes1.html#T2">CLASSES1:2</a>, <a class="ref" href="card_3.html#D4">CARD_3:def 4</a></i>;<br/>
<a NAME="E10:21_1_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="zf_refle.html#K1" target="_self">union</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="classes2.html#T65">CLASSES2:65</a></i>;<br/>
<b>hence </b><a NAME="E11:21_1_1"/>
 <a href="zf_refle.html#K1" target="_self">union</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> is    <a href="ordinal4.html#M1">Ordinal</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="ordinal4.html#D2">ORDINAL4:def 2</a></i>;<br/>


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