Theorems · Theorem · logic and foundations
Equiv.image_symm_eq_preimage
∀ {α : Type u_1} {β : Type u_2} (e : α ≃ β) (s : Set β), ⇑e.symm '' s = ⇑e ⁻¹' s- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 3,681
- Set.extproof · cited by 2,266
- Equiv.right_invproof · cited by 68
- Equiv.left_invproof · cited by 59
- Set.mem_image_iff_of_inverseproof · cited by 3
Cited by17
Results whose statement or proof uses this declaration.
- Equiv.image_eq_preimage_symmproof · cited by 64
- Set.preimage_smulproof · cited by 15
- Set.preimage_vaddproof · cited by 14
- Set.smul_set_subset_iff_subset_inv_smul_setproof · cited by 9
- Equiv.induced_symmproof · cited by 3
- Set.vadd_set_subset_iff_subset_neg_vadd_setproof · cited by 2
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1
- IsClosed.mem_of_ge_of_forall_exists_ltproof · cited by 1
- image_latticeClosure'proof · cited by 1
- CompactCoherentification.isCompact_iffproof · cited by 1
- MeasurableEquiv.image_symmproof · cited by 1
- WithTopology.image_ofTopologyproof · cited by 1