Theorems · Definition · logic and foundations
Equiv.image
{α : Type u_3} → {β : Type u_4} → (e : α ≃ β) → (s : Set α) → ↑s ≃ ↑(⇑e '' s)A set is equivalent to its image under an equivalence.
- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement and proof · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- Equiv.symmproof · cited by 3,681
Cited by25
Results whose statement or proof uses this declaration.
- LinearMap.trace_conj'proof · cited by 8
- Homeomorph.imageproof · cited by 4
- AddEquiv.addSubmonoidMapproof · cited by 3
- MulEquiv.submonoidMapproof · cited by 3
- Polynomial.rootsExpandPowEquivRootsproof · cited by 2
- AddEquiv.subsemigroupMapproof · cited by 2
- MulEquiv.subsemigroupMapproof · cited by 2
- IsTranscendenceBasis.of_isAlgebraic_adjoin_insert_sdiffproof · cited by 2
- Polynomial.rootsExpandEquivRootsproof · cited by 1
- Equiv.image_apply_coestatement and proof · cited by 1
- Cardinal.lift_mk_le_lift_mk_mul_of_lift_mk_preimage_leproof · cited by 1
- Equiv.image_strictAntistatement · cited by 1