Theorems · Theorem · order theory
disjointed_eq_inf_compl
∀ {α : Type u_1} {ι : Type u_2} [inst : CompleteBooleanAlgebra α] [inst_1 : Preorder ι]
[inst_2 : LocallyFiniteOrderBot ι] (f : ι → α) (i : ι), disjointed f i = f i ⊓ ⨅ j, ⨅ (_ : j < i), (f j)ᶜ- Defined in
- Mathlib.Order.Disjointed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Compl.complstatement and proof · cited by 2,925
- iSupproof · cited by 2,415
- iInfstatement and proof · cited by 1,690
- LocallyFiniteOrderBotstatement and proof · cited by 286
- iSup_congr_Propproof · cited by 247
- Finset.Iioproof · cited by 147
- disjointedstatement · cited by 64
- CompleteBooleanAlgebrastatement and proof · cited by 32
- Finset.sup_eq_iSupproof · cited by 30
- sdiff_eqproof · cited by 18
- compl_iSupproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- disjointed_eq_inter_complproof · cited by 1