reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i for Integer;
reserve r for Real;
reserve p for Prime;

theorem Th17:
  for r being Complex holds OddEvenPowers(r,1) = <*1*>
  proof
    let r be Complex;
A1: len OddEvenPowers(r,1) = 1 by Def3;
    OddEvenPowers(r,1).(2*0+1) = r|^(1-1) by Def3;
    hence thesis by A1,FINSEQ_1:40,NEWTON:4;
  end;
