Theorems · Definition · group theory
AddConstEquiv.equivUnits
{G : Type u_1} → [inst : Add G] → {a : G} → AddConstEquiv G G a a ≃* (AddConstMap G G a a)ˣGroup equivalence between G ≃+c[a, a] G and the units of G →+c[a, a] G.
- Defined in
- Mathlib.Algebra.AddConstMap.Equiv
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equivproof · cited by 8,337
- Unitsstatement and proof · cited by 2,804
- MulEquivstatement · cited by 1,142
- MulEquiv.symmproof · cited by 482
- Units.mapproof · cited by 95
- AddConstMapstatement and proof · cited by 32
- AddConstEquivstatement · cited by 31
- MonoidHom.toHomUnitsproof · cited by 9
- Equiv.Perm.equivUnitsEndproof · cited by 4
- AddConstEquiv.toAddConstMapHomproof · cited by 1
- AddConstMap.toEndproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- AddConstEquiv.coe_val_equivUnits_applystatement and proof · cited by 0
- AddConstEquiv.coe_val_inv_equivUnits_applystatement and proof · cited by 0
- AddConstEquiv.equivUnits_symm_apply_applystatement and proof · cited by 0
- AddConstEquiv.equivUnits_symm_apply_symm_applystatement and proof · cited by 0