Theorems · Theorem · logic and foundations
Equiv.ofInjective_symm_apply
∀ {α : Sort u_3} {β : Type u_4} {f : α → β} (hf : Function.Injective f) (a : α),
(Equiv.ofInjective f hf).symm ⟨f a, ⋯⟩ = a- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.symmstatement and proof · cited by 3,681
- Equiv.injectiveproof · cited by 464
- Equiv.apply_symm_applyproof · cited by 346
- Equiv.ofInjectivestatement and proof · cited by 64
- Equiv.ofInjective_applyproof · cited by 10
Cited by8
Results whose statement or proof uses this declaration.
- Module.Basis.reindexRange_selfproof · cited by 4
- Equiv.Perm.exists_extending_pairproof · cited by 2
- MvPolynomial.killCompl_comp_renameproof · cited by 1
- TopCat.binaryCofan_isColimit_iffproof · cited by 1
- CategoryTheory.Limits.Types.binaryCofan_isColimit_iffproof · cited by 0
- LinearIndependent.span_repr_eqproof · cited by 0
- PrincipalSeg.subrelIso_applyproof · cited by 0
- Equiv.coe_ofInjective_symmproof · cited by 0