reserve n, k, r, m, i, j for Nat;

theorem Th51:
  for k being Nat holds 2 * k in EvenNAT & not 2 * k + 1 in EvenNAT
proof
  let k be Nat;
  thus 2 * k in EvenNAT;
  assume 2 * k + 1 in EvenNAT;
  then ex p being Nat st 2 * k + 1 = 2 * p;
  hence thesis;
end;
