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chore(order/boolean_algebra) : compl_involutive (#8357)
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Co-authored-by: Eric <37984851+ericrbg@users.noreply.github.com>
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ericrbg and ericrbg committed Jul 18, 2021
1 parent f45df47 commit 865e36b
Showing 1 changed file with 6 additions and 1 deletion.
7 changes: 6 additions & 1 deletion src/order/boolean_algebra.lean
Expand Up @@ -577,8 +577,13 @@ is_compl_bot_top.compl_eq
@[simp] theorem compl_compl (x : α) : xᶜᶜ = x :=
is_compl_compl.symm.compl_eq

@[simp] theorem compl_involutive : function.involutive (compl : α → α) := compl_compl

theorem compl_bijective : function.bijective (compl : α → α) :=
compl_involutive.bijective

theorem compl_injective : function.injective (compl : α → α) :=
function.involutive.injective compl_compl
compl_involutive.injective

@[simp] theorem compl_inj_iff : xᶜ = yᶜ ↔ x = y :=
compl_injective.eq_iff
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