Theorems · Theorem · order theory
iInf_sup_of_monotone
∀ {α : Type u} [inst : Order.Coframe α] {ι : Type u_1} [inst_1 : Preorder ι] [IsCodirectedOrder ι] {f g : ι → α},
Monotone f → Monotone g → ⨅ i, f i ⊔ g i = (⨅ i, f i) ⊔ ⨅ i, g i- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- iInfstatement and proof · cited by 1,690
- Monotonestatement and proof · cited by 1,397
- LE.le.antisymm'proof · cited by 104
- IsCodirectedOrderstatement and proof · cited by 95
- sup_le_supproof · cited by 48
- Order.Coframestatement and proof · cited by 38
- directed_ofproof · cited by 14
- iInf_mono'proof · cited by 10
- iInf_sup_iInfproof · cited by 3
- iInf_sup_iInf_leproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Set.Finite.iInf_biSup_of_monotoneproof · cited by 2
- iInf_sup_of_antitoneproof · cited by 1
- Set.iInter_union_of_monotoneproof · cited by 0