Theorems · Theorem · order theory
compl_sup_distrib
∀ {α : Type u_2} [inst : HeytingAlgebra α] (a b : α), (a ⊔ b)ᶜ = aᶜ ⊓ bᶜ- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- HeytingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- HImp.himpproof · cited by 153
- HeytingAlgebrastatement and proof · cited by 108
- sup_himp_distribproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- compl_supproof · cited by 8
- compl_symmDiffproof · cited by 2
- compl_compl_inf_distribproof · cited by 2
- compl_compl_himp_distribproof · cited by 1
- compl_image_latticeClosureproof · cited by 1