apply le_defn.mpr
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n₁ n₂ m : ℕ
x✝ : n₁ ≤ n₂
d : ℕ
h✝ : n₁ + d ≃ n₂
⊢ n₁ + m ≤ n₂ + m
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n₁ n₂ m : ℕ
x✝ : n₁ ≤ n₂
d : ℕ
h✝ : n₁ + d ≃ n₂
⊢ ∃ k, n₁ + m + k ≃ n₂ + m