Mathlib Map

Theorems · Theorem · order theory

Finset.inf_def

∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf α] [inst_1 : OrderTop α] {s : Finset β} {f : β → α},
  s.inf f = (Multiset.map f s.val).inf
Defined in
Mathlib.Data.Finset.Lattice.Fold
Cited by
1 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
SemilatticeInfOrderTop
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

List.foldr_inf_eq_inf_toFinset · cited by 0List.foldr_inf_eq_inf_toF…Finset · cited by 13712FinsetMultiset.map · cited by 876Multiset.mapSemilatticeInf · cited by 634SemilatticeInfOrderTop · cited by 493OrderTopFinset.val · cited by 438Finset.valFinset.inf · cited by 219Finset.infMultiset.inf · cited by 19Multiset.infFinset.inf_defCITED BYCITES

Cites7

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

Cited by1

Results whose statement or proof uses this declaration.