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<b>let </b><font color="Maroon" title="c1">r</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:6_1"/>
( <font color="Maroon" title="c1">r</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Maroon" title="c1">r</font> is <a href="ordinal1.html#V5" title="ORDINAL1:attr.5">T-Sequence-like</a> )
 ;<br/><a NAME="E2:6_1"/><b>then </b>
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">r</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">r</font> is   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> )
 <b>by </b><i><a class="ref" href="finset_1.html#T29" title="FINSET_1:th.29">FINSET_1:29</a>, <a class="ref" href="ordinal1.html#D7" title="ORDINAL1:def.7">ORDINAL1:def 7</a></i>;<br/><a NAME="E3:6_1"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 <b>by </b><i><a class="ref" href="card_4.html#T7" title="CARD_4:th.7">CARD_4:7</a></i>;<br/><b>hence </b><a NAME="E4:6_1"/>
 ex <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">n</font>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:6"/>
 ex <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">n</font>
 ;<br/>

<b>hence </b><a NAME="E3:6"/>
( <font color="Maroon" title="c1">r</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Maroon" title="c1">r</font> is <a href="ordinal1.html#V5" title="ORDINAL1:attr.5">T-Sequence-like</a> )
 <b>by </b><i><a class="ref" href="finset_1.html#T29" title="FINSET_1:th.29">FINSET_1:29</a>, <a class="ref" href="ordinal1.html#D7" title="ORDINAL1:def.7">ORDINAL1:def 7</a></i>;<br/>


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