theorem Std.PRange.Nat.succ_eq {n : Nat} : succ n = n + 1

theorem Std.PRange.Nat.toList_Rco_succ_succ {m n : Nat} : ((m + 1)...n + 1).toList = List.map (fun (x : Nat) => x + 1) (m...n).toList

@[deprecated Std.PRange.Nat.toList_Rco_succ_succ (since := "2025-08-22")]

theorem Std.PRange.Nat.ClosedOpen.toList_succ_succ {m n : Nat} : ((m + 1)...n + 1).toList = List.map (fun (x : Nat) => x + 1) (m...n).toList

@[simp]

theorem Std.PRange.Nat.size_Rcc {a b : Nat} : (a...=b).size = b + 1 - a

@[simp]

theorem Std.PRange.Nat.size_Rco {a b : Nat} : (a...b).size = b - a

@[simp]

theorem Std.PRange.Nat.size_Roc {a b : Nat} : (a<...=b).size = b - a

@[simp]

theorem Std.PRange.Nat.size_Roo {a b : Nat} : (a<...b).size = b - a - 1

@[simp]

theorem Std.PRange.Nat.size_Ric {b : Nat} : (*...=b).size = b + 1

@[simp]

theorem Std.PRange.Nat.size_Rio {b : Nat} : (*...b).size = b