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;
