Boolean quantifiers

This proves a few properties about List.all and List.any, which are the Bool universal and existential quantifiers. Their definitions are in core Lean.

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theorem List.all_iff_forall {α : Type u_1} {l : List α} {p : α → Bool} : List.all l p = true ↔ ∀ (a : α), a ∈ l → p a = true

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theorem List.all_iff_forall_prop {α : Type u_1} {p : α → Prop} [inst : DecidablePred p] {l : List α} : (List.all l fun a => decide (p a)) = true ↔ (a : α) → a ∈ l → p a

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theorem List.any_iff_exists {α : Type u_1} {l : List α} {p : α → Bool} : List.any l p = true ↔ ∃ a, a ∈ l ∧ p a = true

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theorem List.any_iff_exists_prop {α : Type u_1} {p : α → Prop} [inst : DecidablePred p] {l : List α} : (List.any l fun a => decide (p a)) = true ↔ ∃ a, a ∈ l ∧ p a

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theorem List.any_of_mem {α : Type u_1} {l : List α} {a : α} {p : α → Bool} (h₁ : a ∈ l) (h₂ : p a = true) : List.any l p = true