
theorem :: Problem 54
  for x,y,z being Nat st
    y = 5 * x + 2 & z = 7 * x + 3 holds
      x * (x + 1), y * (y + 1), z * (z + 1) form_an_AP &
        x < y < z
  proof
    let x,y,z be Nat;
    assume
A1: y = 5 * x + 2 & z = 7 * x + 3;
t0: 1 * x <= 5 * x by XREAL_1:64;
TT: 5 * x + 0 < 5 * x + 2 by XREAL_1:8;
    5 * x <= 7 * x by XREAL_1:64;
    hence thesis by TT,A1,XREAL_1:8,t0,XXREAL_0:2;
  end;
