Theorems · Theorem · order theory
iInf_sup_le_iInf_sup
∀ {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
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Cites5
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
- iInf_leproof · cited by 104
- le_iInfproof · cited by 102
- sup_le_sup_rightproof · cited by 14
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