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Theorems · Theorem · order theory

Set.injOn_insert

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s : Set α} {a : α},
  a ∉ s → (Set.InjOn f (insert a s) ↔ Set.InjOn f s ∧ f a ∉ f '' s)
Defined in
Mathlib.Data.Set.Function
Cited by
4 results in Mathlib
Foundations
Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Matroid.comap_isBasis_iff · cited by 2Matroid.comap_isBasis_iffIsTranscendenceBasis.of_isAlgebraic_adjoin_insert_sdiff · cited by 2IsTranscendenceBasis.of_i…Set.BijOn.insert_iff · cited by 1BijOn.insert_iffMatroid.comap_closure_eq · cited by 1Matroid.comap_closure_eqSet · cited by 53352SetSet.image · cited by 5609Set.imageSet.InjOn · cited by 543Set.InjOnSet.union_singleton · cited by 107Set.union_singletonSet.disjoint_singleton_right · cited by 17Set.disjoint_singleton_ri…Set.injOn_union · cited by 3Set.injOn_unionSet.injOn_insertCITED BYCITES

Cites6

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Cited by4

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