apply decide_eq_false
α : Type u_1
inst : Finite α
p : α → Prop
inst✝ : DecidablePred p
h : (Finite.any fun x => decide (p x)) = false
⊢ decide (∃ x, p x) = false
case a
α : Type u_1
inst : Finite α
p : α → Prop
inst✝ : DecidablePred p
h : (Finite.any fun x => decide (p x)) = false
⊢ ¬∃ x, p x