reserve N,M,K for ExtNat;

theorem
  N * M = 1 implies N = 1
proof
  assume A1: N * M = 1;
  N <> +infty & M <> +infty
  proof
    assume N = +infty or M = +infty;
    then (N = +infty & (M is zero or M is positive)) or
      (M = +infty & (N is zero or N is positive));
    hence contradiction by A1, XXREAL_3:def 5;
  end;
  then reconsider n = N, m = M as Nat by Th3;
  n * (m qua ExtNat) = 1 by A1;
  hence thesis by NAT_1:15;
end;
