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Theorems · Theorem · combinatorics

Finset.subset_image_iff

∀ {α : Type u_1} {β : Type u_2} [inst : DecidableEq β] {s : Finset α} {t : Finset β} {f : α → β},
  t ⊆ Finset.image f s ↔ ∃ s' ⊆ s, Finset.image f s' = t

If a finset t is a subset of the image of another finset s under f, then it is equal to the image of a subset of s. For the version where s is a set, see subset_set_image_iff.

Defined in
Mathlib.Data.Finset.Image
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Finset.SupIndep.image · cited by 2SupIndep.imageFinset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeFinset.image · cited by 910Finset.imageFinset.coe_image · cited by 222Finset.coe_imageFinset.subset_image_iffCITED BYCITES

Cites4

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Cited by1

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