Theorems · Theorem · order theory
biInf_sup_le_biInf_sup
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] (f : β → α) (s : Set β) (a : α),
(⨅ i ∈ s, f i) ⊔ a ≤ ⨅ i ∈ s, f i ⊔ a- Defined in
- Mathlib.Order.CompleteLattice.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- Assumes
- CompleteLattice
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- le_iInf₂proof · cited by 67
- sup_le_sup_rightproof · cited by 14
- biInf_leproof · cited by 10
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