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chore(order/boolean_algebra): add compl_sdiff (#10722)
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Also mark `sdiff_compl` and `top_sdiff` as `@[simp]`.
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urkud committed Dec 11, 2021
1 parent f9fff7c commit f361373
Showing 1 changed file with 5 additions and 2 deletions.
7 changes: 5 additions & 2 deletions src/order/boolean_algebra.lean
Original file line number Diff line number Diff line change
Expand Up @@ -754,14 +754,17 @@ variables [boolean_algebra α]

theorem sdiff_eq : x \ y = x ⊓ yᶜ := boolean_algebra.sdiff_eq x y

theorem sdiff_compl : x \ yᶜ = x ⊓ y := by rw [sdiff_eq, compl_compl]
@[simp] theorem sdiff_compl : x \ yᶜ = x ⊓ y := by rw [sdiff_eq, compl_compl]

theorem top_sdiff : ⊤ \ x = xᶜ := by rw [sdiff_eq, top_inf_eq]
@[simp] theorem top_sdiff : ⊤ \ x = xᶜ := by rw [sdiff_eq, top_inf_eq]
@[simp] theorem sdiff_top : x \ ⊤ = ⊥ := by rw [sdiff_eq, compl_top, inf_bot_eq]

@[simp] lemma sup_inf_inf_compl : (x ⊓ y) ⊔ (x ⊓ yᶜ) = x :=
by rw [← sdiff_eq, sup_inf_sdiff _ _]

@[simp] lemma compl_sdiff : (x \ y)ᶜ = xᶜ ⊔ y :=
by rw [sdiff_eq, compl_inf, compl_compl]

end boolean_algebra

instance Prop.boolean_algebra : boolean_algebra Prop :=
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