Theorems · Theorem · order theory
le_iSup_inf_iSup
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] (f g : ι → α), ⨆ i, f i ⊓ g i ≤ (⨆ i, f i) ⊓ ⨆ i, g i- Defined in
- Mathlib.Order.CompleteLattice.Lemmas
- Cited by
- 2 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.
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- inf_le_leftproof · cited by 286
- inf_le_rightproof · cited by 238
- le_infproof · cited by 107
- iSup_monoproof · cited by 37
Cited by2
Results whose statement or proof uses this declaration.
- iSup_inf_of_monotoneproof · cited by 3
- Set.iUnion_inter_subsetproof · cited by 0