reserve x for set;
reserve a, b, c for Real;
reserve m, n, m1, m2 for Nat;
reserve k, l for Integer;
reserve p, q for Rational;
reserve s1, s2 for Real_Sequence;
reserve r, u for Real,
  k for Nat;

theorem Th94:
  for n,m,l be Nat st n divides m & n divides l holds n divides m-l
proof
  let n,m,l be Nat;
  assume that
A1: n divides m and
A2: n divides l;
A3: -l =-n*(l div n) by A2,NAT_D:3
    .=n*(-(l div n));
  m = n * (m div n) by A1,NAT_D:3;
  then m - l =n * ((m div n) + -(l div n)) by A3;
  hence thesis by INT_1:def 3;
end;
