Mathlib Map

Theorems · Theorem · order theory

OrderIso.map_sInf

∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] [inst_1 : CompleteLattice β] (f : α ≃o β) (s : Set α),
  f (sInf s) = ⨅ a ∈ s, f a
Defined in
Mathlib.Order.CompleteLattice.Basic
Cited by
3 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
CompleteLatticeCompleteLattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

OrderIso.map_sInf_eq_sInf_symm_preimage · cited by 18OrderIso.map_sInf_eq_sInf…sSup_inv · cited by 1sSup_invsSup_neg · cited by 1sSup_negDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetiInf · cited by 1690iInfCompleteLattice · cited by 1048CompleteLatticeInfSet.sInf · cited by 935InfSet.sInfOrderIso · cited by 874OrderIsoOrderIso.map_iInf · cited by 25OrderIso.map_iInfsInf_eq_iInf · cited by 22sInf_eq_iInfOrderIso.map_sInfCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.