Mathlib Map

Theorems · Theorem

Function.Injective.of_comp_iff

∀ {α : Sort u_1} {β : Sort u_2} {γ : Sort u_3} {f : α → β},
  Function.Injective f → ∀ (g : γ → α), Function.Injective (f ∘ g) ↔ Function.Injective g
Defined in
Mathlib.Logic.Function.Basic
Cited by
14 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
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Around this declaration

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

Function.Bijective.of_comp_iff' · cited by 26Bijective.of_comp_iff'AlgebraicIndependent.algebraMap_injective · cited by 9AlgebraicIndependent.alge…Topology.IsEmbedding.of_comp_iff · cited by 9IsEmbedding.of_comp_iffIsUniformEmbedding.of_comp_iff · cited by 8IsUniformEmbedding.of_com…Set.preimage_injective · cited by 3Set.preimage_injectiveEmbeddingLike.comp_injective · cited by 3EmbeddingLike.comp_inject…Topology.IsOpenEmbedding.of_comp_iff · cited by 2IsOpenEmbedding.of_comp_i…ContinuousLinearMap.toContinuousAddMonoidHom_injective · cited by 2ContinuousLinearMap.toCon…Submonoid.pow_right_injective_iff_pow_injective · cited by 1Submonoid.pow_right_injec…alternatingGroup.ofSubtype_injective · cited by 1alternatingGroup.ofSubtyp…SSet.prodStdSimplex.nonDegenerate_iff_injective_objEquiv · cited by 1prodStdSimplex.nonDegener…PLift.map_injective · cited by 0PLift.map_injectiveLinearMap.separatingLeft_dualProd · cited by 0LinearMap.separatingLeft_…ULift.map_injective · cited by 0ULift.map_injectiveFunction.Injective.of_comp · cited by 82Injective.of_compInjective.of_comp_iffCITED BYCITES

Cites1

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Cited by14

Results whose statement or proof uses this declaration.