Theorems · Theorem · logic and foundations
Equiv.image_eq_preimage_symm
∀ {α : Type u_1} {β : Type u_2} (e : α ≃ β) (s : Set α), ⇑e '' s = ⇑e.symm ⁻¹' s- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 15 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
- Set.preimagestatement · cited by 4,946
- Equiv.symmstatement and proof · cited by 3,681
- Equiv.image_symm_eq_preimageproof · cited by 17
Cited by64
Results whose statement or proof uses this declaration.
- finsum_eq_sum_of_support_subsetproof · cited by 28
- Set.mem_image_equivproof · cited by 22
- finprod_eq_prod_of_mulSupport_subsetproof · cited by 21
- Set.subset_smul_set_iffproof · cited by 13
- OrderIso.image_eq_preimage_symmproof · cited by 13
- Homeomorph.image_symmproof · cited by 13
- Homeomorph.preimage_symmproof · cited by 9
- Metric.Snowflaking.image_ofSnowflaking_eq_preimageproof · cited by 6
- Metric.Snowflaking.image_toSnowflaking_eq_preimageproof · cited by 6
- ContinuousLinearEquiv.image_eq_preimage_symmproof · cited by 5
- LinearEquiv.image_eq_preimage_symmproof · cited by 5
- AffineEquiv.image_symmproof · cited by 4