Nat.mul_one (n : Nat) : n * 1 = n Nat.not_le {a b : Nat} : ¬a ≤ b ↔ b < a and_not_self {a : Prop} : ¬(a ∧ ¬a) Nat.add_one_ne_zero (n : Nat) : n + 1 ≠ 0 Nat.zero_le (n : Nat) : 0 ≤ n @LE.le Nat _ 0 _ Nat.succ_eq_add_one (n : Nat) : n.succ = n + 1 succ _ Nat.pred_succ (n : Nat) : n.succ.pred = n pred _ List.getElem?_nil.{u_1} {α : Type u_1} {i : Nat} : [][i]? = none @getElem? (List _) Nat _ _ _ (@nil _) _ List.or_cons {a : Bool} {l : List Bool} : (a :: l).or = (a || l.or) List.or (@cons Bool _ _) List.not_mem_nil.{u_1} {α : Type u_1} {a : α} : ¬a ∈ [] @Membership.mem _ (List _) _ (@nil _) _ List.mem_cons.{u_1} {α✝ : Type u_1} {b : α✝} {l : List α✝} {a : α✝} : a ∈ b :: l ↔ a = b ∨ a ∈ l @Membership.mem _ (List _) _ (@cons _ _ _) _ List.singleton_append.{u_1} {α✝ : Type u_1} {x : α✝} {l : List α✝} : [x] ++ l = x :: l @HAppend.hAppend (List _) (List _) (List _) _ (@cons _ _ (@nil _)) _ List.append_nil.{u} {α : Type u} (as : List α) : as ++ [] = as @Eq (List _) (@HAppend.hAppend (List _) (List _) (List _) _ _ _) (@nil _) List.mapM_nil.{u_1, u_2, u_3} {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_1} [Monad m] {f : α → m β} : mapM f [] = pure [] @mapM _ _ _ _ _ (@nil _) Nat.instIdempotentOpGcd : Std.IdempotentOp gcd @Std.IdempotentOp Nat gcd List.instDecidableMemOfLawfulBEq.{u} {α : Type u} [BEq α] [LawfulBEq α] (a : α) (as : List α) : Decidable (a ∈ as) Decidable (@Membership.mem _ (List _) _ _ _) List.instForIn'InferInstanceMembershipOfMonad.{u_1, u_2, u_3} {m : Type u_1 → Type u_2} {α : Type u_3} [Monad m] : ForIn' m (List α) α inferInstance ForIn' _ (List _) _ (@instMembership _) @Eq Nat (bar _ (@OfNat.ofNat Nat _ _)) (@default Nat _) bar _ _ @Exists Nat @Eq Nat _ 0