Theorems · Theorem · order theory
le_compl_iff_disjoint_right
∀ {α : Type u_2} [inst : HeytingAlgebra α] {a b : α}, a ≤ bᶜ ↔ Disjoint a b- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- HeytingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- Compl.complstatement · cited by 2,925
- Disjointstatement and proof · cited by 2,201
- HeytingAlgebrastatement and proof · cited by 108
- disjoint_iff_inf_leproof · cited by 64
- le_himp_iffproof · cited by 19
- himp_botproof · cited by 9
Cited by10
Results whose statement or proof uses this declaration.
- Set.subset_compl_iff_disjoint_rightproof · cited by 17
- le_compl_iff_disjoint_leftproof · cited by 7
- le_compl_commproof · cited by 4
- compl_topproof · cited by 4
- Disjoint.le_compl_rightproof · cited by 3
- disjoint_compl_right_iffproof · cited by 2
- compl_compl_inf_distribproof · cited by 2
- compl_compl_himp_distribproof · cited by 1
- Finset.subset_compl_iff_disjoint_rightproof · cited by 0
- Heyting.IsRegular.disjoint_compl_right_iffproof · cited by 0