∀ {α : Type u_1} [inst : LinearOrder α] {P : α → Prop} {b c : α} [inst_1 : AddCommMagma α] [CanonicallyOrderedAdd α]
  [AddLeftMono α] [IsLeftCancelAdd α], (∀ a ≤ b + c, P a) ↔ (∀ a < c, P a) ∧ ∀ d ≤ b, P (d + c)