Theorems · Theorem · group theory
zpow_negSucc
∀ {G : Type u_1} [inst : DivInvMonoid G] (a : G) (n : ℕ), a ^ Int.negSucc n = (a ^ (n + 1))⁻¹- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 92 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- DivInvMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- zpow_natCastproof · cited by 271
- DivInvMonoidstatement and proof · cited by 103
- DivInvMonoid.zpow_neg'proof · cited by 4
Cited by92
Results whose statement or proof uses this declaration.
- zpow_negproof · cited by 198
- one_zpowproof · cited by 44
- zpow_ne_zeroproof · cited by 30
- zpow_mulproof · cited by 27
- Int.coe_negOnePowproof · cited by 24
- zero_zpowproof · cited by 19
- zpow_add_oneproof · cited by 18
- MeromorphicAt.zpowproof · cited by 14
- mul_zpowproof · cited by 12
- zpow_neg_oneproof · cited by 11
- inv_zpowproof · cited by 10
- zpow_memproof · cited by 8