Theorems · Definition · group theory
WithZero.logEquiv
{G : Type u_5} → [inst : AddGroup G] → (WithZero (Multiplicative G))ˣ ≃ GThe logarithm as an equivalence between (Gᵐ⁰)ˣ and G.
- Defined in
- Mathlib.Algebra.GroupWithZero.WithZero
- Cited by
- 4 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.
Cites9
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
- Equiv.transproof · cited by 337
- Multiplicative.toAddproof · cited by 161
- MulEquiv.toEquivproof · cited by 126
- WithZero.unitsWithZeroEquivproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- WithZero.logOrderIsoproof · cited by 3
- WithZero.logEquiv_applystatement · cited by 1
- WithZero.logEquiv_symmstatement · cited by 0
- WithZero.logEquiv_unitsMk0statement · cited by 0
- WithZero.expEquiv_symmstatement · cited by 0