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Theorems · Theorem

DFunLike.coe_injective

∀ {F : Sort u_1} {α : outParam (Sort u_2)} {β : outParam (α → Sort u_3)} [self : DFunLike F α β],
  Function.Injective DFunLike.coe

The coercion to functions must be injective.

Defined in
Mathlib.Data.FunLike.Basic
Cited by
161 results in Mathlib
Foundations
Depth 3 from the axioms, rests on 5 definitions · uses no axioms
Assumes
DFunLike
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

DFunLike.ext · cited by 240DFunLike.extDFunLike.ext' · cited by 78DFunLike.ext'Finsupp.single_zero · cited by 63Finsupp.single_zeroOrderHom.ext · cited by 55OrderHom.extOrderIso.ext · cited by 23OrderIso.extDFunLike.coe_fn_eq · cited by 18DFunLike.coe_fn_eqCategoryTheory.GrothendieckTopology.ext · cited by 12GrothendieckTopology.extFunction.Exact.linearMap_comp_eq_zero · cited by 9Exact.linearMap_comp_eq_z…ContinuousMap.isUniformEmbedding_toUniformOnFunIsCompact · cited by 8ContinuousMap.isUniformEm…DFinsupp.single_zero · cited by 8DFinsupp.single_zeroMulEquiv.toMonoidHom_injective · cited by 6MulEquiv.toMonoidHom_inje…IncidenceAlgebra.ext · cited by 6IncidenceAlgebra.extFinsupp.univ_sum_single · cited by 6Finsupp.univ_sum_singleGenLoop.ext · cited by 5GenLoop.extRestrictedProduct.isEmbedding_coe_of_principal · cited by 5RestrictedProduct.isEmbed…DFunLike.coe · cited by 62936DFunLike.coeDFunLike · cited by 576DFunLikeDFunLike.coe_injectiveCITED BYCITES

Cites2

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

Cited by162

Results whose statement or proof uses this declaration.