reserve a, b for Real,
  r for Real,
  rr for Real,
  i, j, n for Nat,
  M for non empty MetrSpace,
  p, q, s for Point of TOP-REAL 2,
  e for Point of Euclid 2,
  w for Point of Euclid n,
  z for Point of M,
  A, B for Subset of TOP-REAL n,
  P for Subset of TOP-REAL 2,
  D for non empty Subset of TOP-REAL 2;
reserve a, b for Real;

theorem Th11:
  for i be Nat for F being FinSequence of REAL st i in dom abs F &
  a = F.i holds (abs F).i = |.a.|
proof
  let i be Nat;
  let F be FinSequence of REAL such that
A1: i in dom abs F and
A2: a = F.i;
  (abs F).i = absreal.a by A1,A2,FUNCT_1:12;
  hence thesis by EUCLID:def 2;
end;
