Theorems · Theorem · logic and foundations
Set.mem_image_equiv
∀ {α : Type u_3} {β : Type u_4} {S : Set α} {f : α ≃ β} {x : β}, x ∈ ⇑f '' S ↔ f.symm x ∈ S- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement and proof · cited by 8,337
- Set.imagestatement · cited by 5,609
- Equiv.symmstatement · cited by 3,681
- Set.ext_iffproof · cited by 90
- Equiv.image_eq_preimage_symmproof · cited by 64
Cited by22
Results whose statement or proof uses this declaration.
- Set.mem_vadd_set_iff_neg_vadd_memproof · cited by 24
- Set.mem_smul_set_iff_inv_smul_memproof · cited by 18
- MvPowerSeries.coeff_eq_zero_of_lt_lexOrderproof · cited by 5
- ZSpan.map_fundamentalDomainproof · cited by 2
- AddSubgroup.mem_map_equivproof · cited by 2
- Subgroup.mem_map_equivproof · cited by 2
- MonoidAlgebra.single_mem_span_singleproof · cited by 1
- AddMonoidAlgebra.single_mem_span_singleproof · cited by 1
- AddSubmonoid.mem_map_equivproof · cited by 0
- AddEquiv.addSubgroupMap_symm_applystatement · cited by 0
- AddSubsemigroup.mem_map_equivproof · cited by 0
- Subring.mem_map_equivproof · cited by 0