
theorem Th1:
  for n,m be Nat st n <> 0 & m <> 0 holds n*m - n - m + 1 >= 0
proof
  let n,m be Nat;
  assume that
A1: n <> 0 and
A2: m <> 0;
  m >= 0+1 by A2,NAT_1:13;
  then
A3: m-1 >= 0+1-1;
  n >= 0+1 by A1,NAT_1:13;
  then n-1 >= 0+1-1;
  then (n-1)*(m-1) >= 0 by A3;
  hence thesis;
end;
