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Theorems · Theorem · combinatorics

Finset.mem_image_of_mem

∀ {α : Type u_1} {β : Type u_2} [inst : DecidableEq β] {s : Finset α} (f : α → β) {a : α},
  a ∈ s → f a ∈ Finset.image f s
Defined in
Mathlib.Data.Finset.Image
Cited by
81 results in Mathlib
Foundations
Depth 75 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.mem_sym_iff · cited by 9Finset.mem_sym_iffHasSum.sigma · cited by 8HasSum.sigmaFinset.exists_max_image · cited by 8Finset.exists_max_imageFinset.sum_of_injOn · cited by 8Finset.sum_of_injOnIsAlgebraic.restrictScalars · cited by 6IsAlgebraic.restrictScala…SimpleGraph.minDegree_le_degree · cited by 6SimpleGraph.minDegree_le_…HasProd.sigma · cited by 5HasProd.sigmaFinset.image_univ_of_surjective · cited by 5Finset.image_univ_of_surj…Finset.sum_image' · cited by 5Finset.sum_image'Finset.card_eq_sum_card_image · cited by 4Finset.card_eq_sum_card_i…Finset.sum_comp · cited by 4Finset.sum_compFinset.prod_image' · cited by 3Finset.prod_image'Algebra.Generators.map_toComp_ker · cited by 3Generators.map_toComp_kerMatrix.BlockTriangular.det · cited by 3BlockTriangular.detBoxIntegral.Prepartition.restrict_mono · cited by 3Prepartition.restrict_monoFinset · cited by 13712FinsetFinset.image · cited by 910Finset.imageFinset.mem_image · cited by 105Finset.mem_imageFinset.mem_image_of_memCITED BYCITES

Cites3

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

Cited by81

Results whose statement or proof uses this declaration.