Theorems · Theorem · order theory
sup_inf_sdiff
∀ {α : Type u} [inst : GeneralizedBooleanAlgebra α] (x y : α), x ⊓ y ⊔ x \ y = x- Defined in
- Mathlib.Order.BooleanAlgebra.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- GeneralizedBooleanAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- GeneralizedBooleanAlgebrastatement and proof · cited by 204
- GeneralizedBooleanAlgebra.sup_inf_sdiffproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- Set.inter_union_sdiffproof · cited by 23
- Set.sdiff_union_interproof · cited by 19
- sdiff_supproof · cited by 7
- sdiff_uniqueproof · cited by 6
- inf_sdiff_self_rightproof · cited by 6
- inf_sdiff_assocproof · cited by 5
- sdiff_sdiff_rightproof · cited by 4
- sup_inf_inf_sdiffproof · cited by 3
- sdiff_eq_sdiff_iff_inf_eq_infproof · cited by 2
- sdiff_inf_sdiffproof · cited by 2
- sup_inf_inf_complproof · cited by 1
- sup_sdiff_infproof · cited by 1