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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal2.html#NM1">Ordinal-Sequence</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E1:14"/><i><font color="Green">E11</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ordinal2.html#D16">ORDINAL2:def 16</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:14_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K10">"</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:14_1"/><b>then </b><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</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="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/><b>hence </b><a NAME="E3:14_1"/>
<font color="Maroon">c<sub>3</sub></font> is   <a href="ordinal1.html#NM2">Ordinal</a>
 <b>by </b><i><a class="ref" href="ordinal1.html#T23">ORDINAL1:23</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="ordinal1.html#NM2">Ordinal</a> <b>by </b><i><a class="txt" href="ordinal4.html#E2:14_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="ordinal1.html#T23">ORDINAL1:23</a></i>;<br/><b>thus </b><a NAME="E5:14_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K10">"</a> <font color="Maroon">c<sub>2</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></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="E1:14_1_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:14_1_1"/><b>then </b><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="ordinal1.html#NM2">Ordinal</a> <b>by </b><i><a class="ref" href="ordinal1.html#T23">ORDINAL1:23</a></i>;<br/>
<a NAME="E4:14_1_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="ordinal4.html#E2:14_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="ordinal4.html#E2:14_1_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="ordinal1.html#T19">ORDINAL1:19</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> as   <a href="ordinal1.html#NM2">Ordinal</a> ;<br/>
<a NAME="E6:14_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="ordinal4.html#E1:14"><i><font color="Green">E11</font></i></a>, <a class="txt" href="ordinal4.html#E2:14_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="ordinal4.html#E1:14_1_1"><i><font color="Green">E13</font></i></a></i>;<br/>
<a NAME="E7:14_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ordinal4.html#E2:14_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="ordinal1.html#T19">ORDINAL1:19</a></i>;<br/>
<b>hence </b><a NAME="E8:14_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K10">"</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ordinal4.html#E4:14_1_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:14"/>
<font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K10">"</a> <font color="Maroon">c<sub>2</sub></font> is   <a href="ordinal1.html#NM2">Ordinal</a>
 <b>by </b><i><a class="ref" href="ordinal1.html#T31">ORDINAL1:31</a></i>;<br/>


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