Theorems · Theorem · order theory
iSup_inf_le_iSup_inf
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] (f : ι → α) (a : α), ⨆ i, f i ⊓ a ≤ (⨆ i, f i) ⊓ a- Defined in
- Mathlib.Order.CompleteLattice.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
- inf_le_inf_rightproof · cited by 23
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.