reserve x, y, z, s for ExtReal;
reserve i, j for Integer;
reserve n, m for Nat;

theorem Th3:
  0 <= x & x <= y & 0 <= s & s <= z implies x*s <= y*z
  proof
    assume that
A1: 0 <= x and
A2: x <= y and
A3: 0 <= s and
A4: s <= z;
A5: x*s <= y*s by A2,A3,XXREAL_3:71;
    y*s <= y*z by A1,A2,A4,XXREAL_3:71;
    hence thesis by A5,XXREAL_0:2;
  end;
