reserve i,j,k,n for Nat;

theorem
  for f being FinSequence, p,q being set st p in rng f & q in rng f &
  p..f = q..f holds p = q
proof
  let f be FinSequence, p,q be set such that
A1: p in rng f and
A2: q in rng f;
  assume p..f = q..f;
  hence p = f.(q..f) by A1,FINSEQ_4:19
    .= q by A2,FINSEQ_4:19;
end;
