Theorems · Theorem · logic and foundations
Equiv.ofInjective_apply
∀ {α : Sort u_3} {β : Type u_4} (f : α → β) (hf : Function.Injective f) (a : α), (Equiv.ofInjective f hf) a = ⟨f a, ⋯⟩- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- Equiv.ofInjectivestatement and proof · cited by 64
Cited by10
Results whose statement or proof uses this declaration.
- Equiv.ofInjective_symm_applyproof · cited by 8
- Equiv.Perm.exists_extending_pairproof · cited by 2
- Cardinal.extend_functionproof · cited by 2
- MeasurableSpace.measurableEquiv_nat_bool_of_countablyGeneratedproof · cited by 1
- Equiv.Perm.mem_sumCongrHom_range_of_perm_mapsTo_inlproof · cited by 1
- Equiv.ofLeftInverse'_eq_ofInjectiveproof · cited by 0
- Equiv.ofLeftInverse_eq_ofInjectiveproof · cited by 0
- Set.Definable.image_comp_embeddingproof · cited by 0
- Function.Embedding.toEquivRange_eq_ofInjectiveproof · cited by 0
- LinearIndependent.span_repr_eqproof · cited by 0