∀ (R : Type u_2) (Γ₀ : Type u_1) [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] [inst_2 : Nontrivial R]
  [inst_3 : NoZeroDivisors R] [inst_4 : DecidablePred fun x => x = 0] (x y : R),
  (↑1).toFun (x + y) ≤ max ((↑1).toFun x) ((↑1).toFun y)