case msm
m✝ n✝ k : ℕ
P : ℕ → Sort u_1
h : (n : ℕ) → P (n + 1) → P n
m n : ℕ
smn : m + 1 ≤ n
mn : m ≤ n
hP : P n
⊢ m ≤ m + 1
m✝ n✝ k : ℕ
P : ℕ → Sort u_1
h : (n : ℕ) → P (n + 1) → P n
m n : ℕ
smn : m + 1 ≤ n
mn : m ≤ n
hP : P n
⊢ decreasingInduction h mn hP = h m (decreasingInduction h smn hP)
rw [Subsingleton.elim mn (le_trans (le_succ m) smn), decreasingInduction_trans,
  decreasingInduction_succ']
no goals
case msm
m✝ n✝ k : ℕ
P : ℕ → Sort u_1
h : (n : ℕ) → P (n + 1) → P n
m n : ℕ
smn : m + 1 ≤ n
mn : m ≤ n
hP : P n
⊢ m ≤ m + 1
apply Nat.le_succ