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Theorems · Theorem · logic and foundations

Function.Embedding.apply_eq_iff_eq

∀ {α : Sort u_1} {β : Sort u_2} (f : α ↪ β) (x y : α), f x = f y ↔ x = y
Defined in
Mathlib.Logic.Embedding.Basic
Cited by
4 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
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Around this declaration

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

SimpleGraph.CliqueFree.replaceVertex · cited by 3CliqueFree.replaceVertexSimpleGraph.isClique_range_copy_top · cited by 1SimpleGraph.isClique_rang…RootPairing.Hom.coweightHom_injective · cited by 1Hom.coweightHom_injectiveRootPairing.Base.injective_pairingIn · cited by 1Base.injective_pairingInDFunLike.coe · cited by 62936DFunLike.coeFunction.Embedding · cited by 988Function.EmbeddingEmbeddingLike.apply_eq_iff_eq · cited by 20EmbeddingLike.apply_eq_if…Embedding.apply_eq_iff_eqCITED BYCITES

Cites3

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

Cited by4

Results whose statement or proof uses this declaration.