# Documentation

Std.Classes.BEq

## Boolean equality #

class PartialEquivBEq (α : Type u_1) [inst : BEq α] :
• Symmetry for BEq. If a == b then b == a.

symm : ∀ {a b : α}, (a == b) = true(b == a) = true
• Transitivity for BEq. If a == b and b == c then a == c.

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

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

• it is symmetric: a == b → b == a→ b == a
• it is transitive: a == b → b == c → a == c→ b == c → a == c→ a == c.
Instances
@[simp]
theorem beq_eq_false_iff_ne {α : Type u_1} [inst : BEq α] [inst : ] (a : α) (b : α) :
(a == b) = false a b