Boolean equality

class PartialEquivBEq (α : Type u_1) [BEq α] : Prop

• symm : ∀ {a b : α}, (a == b) = true → (b == a) = true

  Symmetry for BEq. If a == b then b == a.

• trans : ∀ {a b c : α}, (a == b) = true → (b == c) = true → (a == c) = true

  Transitivity for BEq. If a == b and b == c then a == c.

PartialEquivBEq α says that the BEq implementation is a partial equivalence relation, that is:

• it is symmetric: a == b → b == a
• it is transitive: a == b → b == c → a == c.

@[simp]

theorem beq_eq_false_iff_ne {α : Type u_1} [BEq α] [LawfulBEq α] (a : α) (b : α) : (a == b) = false ↔ a ≠ b