Theorems · Theorem · logic and foundations
Equiv.eq_preimage_iff_image_eq
∀ {α : Type u_3} {β : Type u_4} (e : α ≃ β) (s : Set α) (t : Set β), s = ⇑e ⁻¹' t ↔ ⇑e '' s = t- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 6 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.
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.bijectiveproof · cited by 132
- Set.eq_preimage_iff_image_eqproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iffproof · cited by 4
- Diffeomorph.image_boundaryproof · cited by 0
- Diffeomorph.image_interiorproof · cited by 0
- IsMaxChain.imageproof · cited by 0
- AddMonoidAlgebra.range_mapproof · cited by 0
- IsMaxAntichain.imageproof · cited by 0