Theorems · Theorem
Equiv.apply_eq_iff_eq
∀ {α : Sort u} {β : Sort v} (f : α ≃ β) {x y : α}, f x = f y ↔ x = y- Defined in
- Mathlib.Logic.Equiv.Defs
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Equivstatement and proof · cited by 8,337
- EquivLike.apply_eq_iff_eqproof · cited by 6
Cited by28
Results whose statement or proof uses this declaration.
- Equiv.Perm.apply_mem_supportproof · cited by 8
- Equiv.Perm.one_lt_card_support_of_ne_oneproof · cited by 4
- Equiv.Perm.Disjoint.support_mulproof · cited by 4
- Equiv.Perm.IsCycle.isCycleOnproof · cited by 3
- OrderIso.apply_eq_iff_eqproof · cited by 3
- Equiv.Perm.mem_support_iff_of_commuteproof · cited by 2
- Subgroup.smul_diff'proof · cited by 2
- Equiv.Perm.card_support_eq_twoproof · cited by 2
- ContinuousMultilinearMap.prod_ext_iffproof · cited by 2
- SSet.S.IsUniquelyCodimOneFace.of_isoproof · cited by 2
- Finpartition.IsEquipartition.exists_partPreservingEquivproof · cited by 1
- Subgroup.ker_restrict_transferFocal_eq_focalSubgroupOfproof · cited by 1