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<span class="kw">reconsider </span><font color="Maroon" title="c4">K</font> = <font color="Maroon" title="c1">phi</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c3">a</font></span>)</span> as   <a href="ordinal2.html#NM1" title="ORDINAL2:NM.1">Ordinal-Sequence</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_refle.html#T9" target="_self" title="ZF_REFLE:th.9">Th11</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">A</font> =  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span> as   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_refle.html#T11" target="_self" title="ZF_REFLE:th.11">Th13</a></span>;<br/>
<a NAME="E3:17_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K2" title="ORDINAL1:func.2">On</a> <font color="Maroon" title="c2">W</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D9" title="ORDINAL1:def.9">ORDINAL1:def 9</a></span>;<br/>
<a NAME="E4:17_1_1"/><span class="kw">then </span>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c3">a</font> &amp;  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes2.html#T25" title="CLASSES2:th.25">CLASSES2:25</a>, <a class="ref" href="relat_1.html#T58" title="RELAT_1:th.58">RELAT_1:58</a></span>;<br/>
<a NAME="E5:17_1_1"/><span class="kw">then </span>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">K</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes1.html#D1" title="CLASSES1:def.1">CLASSES1:def 1</a>, <a class="ref" href="funct_1.html#T56" title="FUNCT_1:th.56">FUNCT_1:56</a></span>;<br/>
<a NAME="E6:17_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes1.html#D1" title="CLASSES1:def.1">CLASSES1:def 1</a></span>;<br/>
<a NAME="E7:17_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A1</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">W</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes2.html#T1" title="CLASSES2:th.1">CLASSES2:1</a></span>;<br/>
<a NAME="E8:17_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T113" title="RELAT_1:th.113">RELAT_1:113</a></span>;<br/>
<a NAME="E9:17_1_1"/><span class="kw">then </span>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">W</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">W</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:17_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="card_1.html#T67" title="CARD_1:th.67">CARD_1:67</a>, <a class="ref" href="ordinal1.html#T12" title="ORDINAL1:th.12">ORDINAL1:12</a>, <a class="ref" href="relat_1.html#T85" title="RELAT_1:th.85">RELAT_1:85</a></span>;<br/>
<a NAME="E10:17_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A2</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes1.html#T1" title="CLASSES1:th.1">CLASSES1:1</a></span>;<br/>
<a NAME="E11:17_1_1"/>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c4">K</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#D4" title="CARD_3:def.4">CARD_3:def 4</a></span>;<br/>
<a NAME="E12:17_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:17_1_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="classes2.html#T59" title="CLASSES2:th.59">CLASSES2:59</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:17_1_1"/>
 <a href="zf_refle.html#K1" title="ZF_REFLE:func.1">union</a> (<font color="Maroon" title="c1">phi</font>,<font color="Maroon" title="c3">a</font>) is   <a href="ordinal4.html#NM1" title="ORDINAL4:NM.1">Ordinal</a> of <font color="Maroon" title="c2">W</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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