Theorem: Finite.exists_eq_false_of_all_eq_false (GMLInit/Class/Finite.lean)

State before:
α✝ : Type ?u.1482
inst : Finite α✝
α : Type u_1
inst✝ : Finite α
p : α → Bool
⊢ Finite.all p = false → ∃ x, p x = false
Tactic:
intro h
State after:
α✝ : Type ?u.1482
inst : Finite α✝
α : Type u_1
inst✝ : Finite α
p : α → Bool
h : Finite.all p = false
⊢ ∃ x, p x = false

State before:
α✝ : Type ?u.1482
inst : Finite α✝
α : Type u_1
inst✝ : Finite α
p : α → Bool
h : Finite.all p = false
⊢ ∃ x, p x = false
Tactic:
match Fin.exists_eq_false_of_all_eq_false h with
| ⟨i, h⟩ => exists (Finite.get α i)
State after:
no goals

State before:
α✝ : Type ?u.1482
inst : Finite α✝
α : Type u_1
inst✝ : Finite α
p : α → Bool
h✝ : Finite.all p = false
i : Fin toArray.size
h : p (Finite.get α i) = false
⊢ ∃ x, p x = false
Tactic:
exists (Finite.get α i)
State after:
no goals