Theorems · Definition · group theory
WithZero.expEquiv
{G : Type u_5} → [inst : AddGroup G] → G ≃ (WithZero (Multiplicative G))ˣThe exponential map as an equivalence between G and (Gᵐ⁰)ˣ.
- Defined in
- Mathlib.Algebra.GroupWithZero.WithZero
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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.
- Equivstatement · cited by 8,337
- AddGroupstatement and proof · cited by 4,410
- Unitsstatement · cited by 2,804
- Multiplicativestatement · cited by 875
- WithZerostatement · cited by 586
- MulEquiv.symmproof · cited by 482
- Equiv.transproof · cited by 337
- Multiplicative.ofAddproof · cited by 237
- MulEquiv.toEquivproof · cited by 126
- WithZero.unitsWithZeroEquivproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- WithZero.expOrderIsoproof · cited by 3
- WithZero.coe_expEquiv_applystatement · cited by 0
- WithZero.expEquiv_symmstatement · cited by 0
- WithZero.logEquiv_symmstatement · cited by 0