Theorems · Theorem · order theory
compl_inf
∀ {α : Type u} {x y : α} [inst : BooleanAlgebra α], (x ⊓ y)ᶜ = xᶜ ⊔ yᶜ- Defined in
- Mathlib.Order.BooleanAlgebra.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- BooleanAlgebra
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
- BooleanAlgebrastatement and proof · cited by 300
- hnot_inf_distribproof · cited by 6
Cited by12
Results whose statement or proof uses this declaration.
- Set.compl_interproof · cited by 26
- compl_sdiffproof · cited by 3
- symmDiff_eq'proof · cited by 2
- BooleanSubalgebra.mem_closure_iff_sup_sdiffproof · cited by 1
- compl_image_latticeClosureproof · cited by 1
- Filter.sdiff_liminfproof · cited by 0
- symmDiff_eq_topproof · cited by 0
- Filter.sdiff_limsupproof · cited by 0
- LowerSet.compl_infproof · cited by 0
- Finset.compls_infsproof · cited by 0
- Finset.compl_interproof · cited by 0
- UpperSet.compl_supproof · cited by 0