Theorems · Theorem · group theory
IsCyclic.mulAutMulEquiv_symm_apply_apply
∀ (G : Type u_2) [inst : Group G] [h : IsCyclic G] (a : (ZMod (Nat.card G))ˣ) (a_1 : G),
((IsCyclic.mulAutMulEquiv G).symm a) a_1 =
(zmodCyclicMulEquiv h)
(Multiplicative.ofAdd
(((↑(AddEquiv.toMultiplicative (ZMod.AddAutEquivUnits (Nat.card G)))).symm a)
(Multiplicative.toAdd ((zmodCyclicMulEquiv h).symm a_1))))- Cited by
- 0 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites22
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
- Equivstatement · cited by 8,337
- Groupstatement and proof · cited by 6,238
- Equiv.symmstatement · cited by 3,681
- Unitsstatement and proof · cited by 2,804
- MulEquivstatement · cited by 1,142
- AddEquivstatement · cited by 1,087
- ZModstatement and proof · cited by 1,024
- Multiplicativestatement · cited by 875
- Nat.cardstatement and proof · cited by 844
- MulEquiv.symmstatement and proof · cited by 482
- Additivestatement · cited by 356
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