Theorems · Theorem · logic and foundations
Equiv.preimage_eq_iff_eq_image
∀ {α : Type u_3} {β : Type u_4} (e : α ≃ β) (s : Set β) (t : Set α), ⇑e ⁻¹' s = t ↔ s = ⇑e '' t- 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.
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.preimage_eq_iff_eq_imageproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Equiv.induced_symmproof · cited by 3
- parallelepiped_comp_equivproof · cited by 3
- Metric.Snowflaking.preimage_toSnowflaking_closedEBallproof · cited by 2
- Metric.Snowflaking.preimage_toSnowflaking_eballproof · cited by 2
- Metric.Snowflaking.preimage_toSnowflaking_ballproof · cited by 1
- MeasurableSpace.measurableEquiv_nat_bool_of_countablyGeneratedproof · cited by 1
- Metric.Snowflaking.preimage_toSnowflaking_closedBallproof · cited by 1
- PowerSeries.coeff_subst_finiteproof · cited by 1