Theorems · Theorem · order theory
compl_sup
∀ {α : Type u_2} [inst : HeytingAlgebra α] {a b : α}, (a ⊔ b)ᶜ = aᶜ ⊓ bᶜ- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- HeytingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Compl.complstatement · cited by 2,925
- HeytingAlgebrastatement and proof · cited by 108
- compl_sup_distribproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Set.compl_unionproof · cited by 30
- BooleanSubalgebra.closure_bot_sup_inductionproof · cited by 2
- Finset.compl_unionproof · cited by 2
- Finset.compls_supsproof · cited by 1
- BooleanSubalgebra.mem_closure_iff_sup_sdiffproof · cited by 1
- LowerSet.compl_supproof · cited by 0
- bihimp_eq_botproof · cited by 0
- UpperSet.compl_infproof · cited by 0