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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>

<b>assume </b><a NAME="E1:2"/><i><font color="Green">E3</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> is <a href="realset1.html#V1">trivial</a>
 ;<br/>

<a NAME="E2:2"/><i><font color="Green">E4</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:2_1"/>
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> or ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> )
 </span><b>by </b><i><a class="txt" href="jordan12.html#E1:2"><i><font color="Green">E3</font></i></a>, <a class="ref" href="realset1.html#D4">REALSET1:def 4</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1"><b>suppose </b></a><a NAME="E1:2_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><a NAME="E2:2_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#T26">FINSEQ_1:26</a></i>;<br/><a NAME="E3:2_1_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/><b>hence </b><a NAME="E4:2_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> is <a href="realset1.html#V1">trivial</a>
 <b>by </b><i><a class="ref" href="realset1.html#D4">REALSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_2"><b>suppose </b></a><a NAME="E1:2_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:2_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> is <a href="realset1.html#V1">trivial</a>
 <b>by </b><i><a class="txt" href="jordan12.html#E2:2"><i><font color="Green">E4</font></i></a>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="finseq_3.html#T22">FINSEQ_3:22</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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