reserve i,j,k,n,m,l,s,t for Nat;
reserve a,b for Real;
reserve F for real-valued FinSequence;
reserve z for Complex;
reserve x,y for Complex;
reserve r,s,t for natural Number;

theorem
  m > 0 & n > 0 implies m lcm n > 0
proof
  assume that
A1: m>0 and
A2: n>0 and
A3: m lcm n <= 0;
A4: (m lcm n) divides m*n by Th47;
  m lcm n = 0 or m lcm n < 0 by A3;
  then ex r being Nat st m*n = 0*r by A4,NAT_D:def 3;
  hence contradiction by A1,A2;
end;
