NeZero typeclass

We give basic facts about the NeZero n typeclass.

theorem not_neZero {R : Type u_1} [Zero R] {n : R} : ¬NeZero n ↔ n = 0

theorem eq_zero_or_neZero {R : Type u_1} [Zero R] (a : R) : a = 0 ∨ NeZero a

@[simp]

theorem zero_ne_one {α : Type u_2} [Zero α] [One α] [NeZero 1] : 0 ≠ 1

@[simp]

theorem one_ne_zero {α : Type u_2} [Zero α] [One α] [NeZero 1] : 1 ≠ 0

theorem ne_zero_of_eq_one {α : Type u_2} [Zero α] [One α] [NeZero 1] {a : α} (h : a = 1) : a ≠ 0

theorem two_ne_zero {α : Type u_2} [Zero α] [OfNat α 2] [NeZero 2] : 2 ≠ 0

theorem three_ne_zero {α : Type u_2} [Zero α] [OfNat α 3] [NeZero 3] : 3 ≠ 0

theorem four_ne_zero {α : Type u_2} [Zero α] [OfNat α 4] [NeZero 4] : 4 ≠ 0

theorem zero_ne_one' (α : Type u_2) [Zero α] [One α] [NeZero 1] : 0 ≠ 1

theorem one_ne_zero' (α : Type u_2) [Zero α] [One α] [NeZero 1] : 1 ≠ 0

theorem two_ne_zero' (α : Type u_2) [Zero α] [OfNat α 2] [NeZero 2] : 2 ≠ 0

theorem three_ne_zero' (α : Type u_2) [Zero α] [OfNat α 3] [NeZero 3] : 3 ≠ 0

theorem four_ne_zero' (α : Type u_2) [Zero α] [OfNat α 4] [NeZero 4] : 4 ≠ 0

theorem NeZero.of_pos {M : Type u_2} {x : M} [Preorder M] [Zero M] (h : 0 < x) : NeZero x