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

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means  <a href="finseq_1.html#K14">Sgm</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_2.html#K1">idseq</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<a NAME="E1:50"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i><a class="ref" href="finseq_3.html#T49" target="_self">Th49</a>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_2.html#T58">FINSEQ_2:58</a></i>;<br/>
<a NAME="E2:50"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1]
 
<b>by </b><i><a class="txt" href="finseq_3.html#E58"><i><font color="Green">Lemma32</font></i></a></i>;<br/>
<a NAME="E3:50"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="finseq_3.html#E1:50"><i><font color="Green">E34</font></i></a>, <a class="txt" href="finseq_3.html#E2:50"><i><font color="Green">E35</font></i></a>);<br/></i>
<a NAME="E4:50"/>
<font color="Maroon">c<sub>1</sub></font> is   <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/>
<b>hence </b><a NAME="E5:50"/>
 <a href="finseq_1.html#K14">Sgm</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_2.html#K1">idseq</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="finseq_3.html#E3:50"><i><font color="Green">E36</font></i></a></i>;<br/>


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