Theorems · Theorem · order theory
sup_inf_inf_compl
∀ {α : Type u} {x y : α} [inst : BooleanAlgebra α], x ⊓ y ⊔ x ⊓ yᶜ = x- Defined in
- Mathlib.Order.BooleanAlgebra.Basic
- Cited by
- 1 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.
Cites4
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
- sdiff_eqproof · cited by 18
- sup_inf_sdiffproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- Order.Ideal.isPrime_of_mem_or_compl_memproof · cited by 1