rcases H with ⟨m, hm, hPm⟩
case pos
α : ℕ → Sort u
P : ℕ → Prop
n : ℕ
ih : ∀ m < n, P m → ∃ x, P x ∧ ∀ z < x, ¬P z
hn : P n
H : ∃ m < n, P m
⊢ ∃ x, P x ∧ ∀ z < x, ¬P z
case pos.intro.intro
α : ℕ → Sort u
P : ℕ → Prop
n : ℕ
ih : ∀ m < n, P m → ∃ x, P x ∧ ∀ z < x, ¬P z
hn : P n
m : ℕ
hm : m < n
hPm : P m
⊢ ∃ x, P x ∧ ∀ z < x, ¬P z