Mathlib Map

Theorems · Theorem

Function.update_injective

∀ {α : Sort u} {β : α → Sort v} [inst : DecidableEq α] (f : (a : α) → β a) (a' : α),
  Function.Injective (Function.update f a')
Defined in
Mathlib.Logic.Function.Basic
Cited by
8 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
DecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.image_update_Ico · cited by 5Set.image_update_IcoPi.single_injective · cited by 5Pi.single_injectiveSet.image_update_Ioo · cited by 4Set.image_update_IooSet.image_update_Ioc · cited by 4Set.image_update_IocPi.mulSingle_injective · cited by 3Pi.mulSingle_injectiveisClosedEmbedding_update · cited by 1isClosedEmbedding_updatePi.nontrivial_at · cited by 0Pi.nontrivial_atPi.infinite_of_exists_right · cited by 0Pi.infinite_of_exists_rig…Function.update · cited by 502Function.updateFunction.update_self · cited by 201Function.update_selfFunction.update_injectiveCITED BYCITES

Cites2

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

Cited by8

Results whose statement or proof uses this declaration.