theorem Th3:
  for p being FinSequence st k in dom p & not k + 1 in dom p holds len p = k
proof
  let p be FinSequence such that
A1: k in dom p and
A2: not k + 1 in dom p;
A3: 1 > k + 1 or k + 1 > len p by A2,FINSEQ_3:25;
A4: 1 + 0 <= k + 1 by XREAL_1:7;
  k <= len p by A1,FINSEQ_3:25;
  hence thesis by A3,A4,NAT_1:22;
end;
