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Theorems · Theorem · order theory

Monotone.map_sInf_le

∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] [inst_1 : CompleteLattice β] {s : Set α} {f : α → β},
  Monotone f → f (sInf s) ≤ ⨅ a ∈ s, f a
Defined in
Mathlib.Order.CompleteLattice.Basic
Cited by
4 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext
Assumes
CompleteLatticeCompleteLattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

nhdsSet_sInter_le · cited by 0nhdsSet_sInter_lenhdsKer_sInter_subset · cited by 0nhdsKer_sInter_subsetAntitone.map_sSup_le · cited by 0Antitone.map_sSup_leClosureOperator.sInf_isClosed · cited by 0ClosureOperator.sInf_isCl…Set · cited by 53352SetiInf · cited by 1690iInfMonotone · cited by 1397MonotoneCompleteLattice · cited by 1048CompleteLatticeInfSet.sInf · cited by 935InfSet.sInfsInf_eq_iInf · cited by 22sInf_eq_iInfMonotone.map_iInf₂_le · cited by 4Monotone.map_iInf₂_leMonotone.map_sInf_leCITED BYCITES

Cites7

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Cited by4

Results whose statement or proof uses this declaration.