reserve a, b, n for Nat,
  r for Real,
  f for FinSequence of REAL;
reserve p for Prime;

theorem Th12:
  <*r*>|^a = <*r|^a*>
proof
A1: len (<*r*>|^a) = len <*r*> by Def1
    .= 1 by FINSEQ_1:40;
  0+1 in Seg (0+1);
  then 1 in dom (<*r*>|^a) by A1,FINSEQ_1:def 3;
  then (<*r*>|^a).1 = (<*r*>.1) |^ a by Def1
    .= r |^ a;
  hence thesis by A1,FINSEQ_1:40;
end;
