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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:46"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:46"/><i><font color="Green">E26</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" target="_self">Necklace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K4">]</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="necklace.html#T19" target="_self">Th19</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E4:46"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K4">]</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="necklace.html#E1:46"><i><font color="Green">E25</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:46"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" target="_self">Necklace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="necklace.html#E2:46"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


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