Theorems · Theorem · order theory
iInf_sup_iInf_le
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] (f g : ι → α), (⨅ i, f i) ⊔ ⨅ i, g i ≤ ⨅ i, f i ⊔ g i- Defined in
- Mathlib.Order.CompleteLattice.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- sup_leproof · cited by 159
- iInf_monoproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- iInf_sup_of_monotoneproof · cited by 3