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<b>set </b><font color="Maroon">phi</font> = <span class="p1">(<span class="default"><a href="ordinal1.html#K3">On</a> <font color="Maroon">W</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <a href="xboole_0.html#K1">{}</a> ;<br/>
<a NAME="E1:41_2_1"/><i><font color="Green">E13</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ordinal1.html#K3">On</a> <font color="Maroon">W</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ordinal1.html#K3">On</a> <font color="Maroon">W</font> &amp; ( for <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K3">On</a> <font color="Maroon">W</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ordinal1.html#K3">On</a> <font color="Maroon">W</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, <a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E2:41_2_1"/><i><font color="Green">E25</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ordinal1.html#K3">On</a> <font color="Maroon">W</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<b>reconsider </b><font color="Maroon">phi</font> = <span class="p1">(<span class="default"><a href="ordinal1.html#K3">On</a> <font color="Maroon">W</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <a href="xboole_0.html#K1">{}</a>  as   <a href="ordinal2.html#NM1">Ordinal-Sequence</a> <b>by </b><i><a class="txt" href="ordinal4.html#E6:41_2_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="ordinal1.html#D7">ORDINAL1:def 7</a></i>;<br/>
<b>take </b>
<font color="Maroon">phi</font>
;<br/>

<b>thus </b><a NAME="E4:41_2_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">phi</font> <a href="hidden.html#R1">=</a>  <a href="ordinal1.html#K3">On</a> <font color="Maroon">W</font>
 <b>by </b><i><a class="txt" href="ordinal4.html#E6:41_2_1"><i><font color="Green">E27</font></i></a></i>;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E5:41_2_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">phi</font>
 ;<br/>

<a NAME="E6:41_2_1"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">phi</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T65">RELAT_1:65</a></i>;<br/>
<a NAME="E7:41_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E8:41_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K3">On</a> <font color="Maroon">W</font>
 <b>by </b><i><a class="ref" href="ordinal4.html#D1" target="_self">Def1</a>, <a class="txt" href="ordinal4.html#E6:41_2_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="ordinal3.html#T10">ORDINAL3:10</a></i>;<br/>


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