Theorems · Theorem · group theory
zpow_zero
∀ {G : Type u_1} [inst : DivInvMonoid G] (a : G), a ^ 0 = 1- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- DivInvMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DivInvMonoidstatement and proof · cited by 103
- DivInvMonoid.zpow_zero'proof · cited by 1
Cited by52
Results whose statement or proof uses this declaration.
- MeromorphicNFAt.meromorphicOrderAt_eq_zero_iffproof · cited by 14
- ModularGroup.coe_T_zpowproof · cited by 9
- MeromorphicAt.meromorphicTrailingCoeffAt_zpowproof · cited by 5
- PadicInt.norm_lt_one_iff_dvdproof · cited by 4
- toMeromorphicNFAt_eq_selfproof · cited by 4
- meromorphicOrderAt_zpowproof · cited by 4
- AnalyticAt.meromorphicTrailingCoeffAt_of_eq_nhdsNEproof · cited by 4
- norm_le_norm_add_norm_inv_mulproof · cited by 3
- padicNorm.int_eq_one_iffproof · cited by 3
- Subgroup.mem_closure_singletonproof · cited by 3
- Subgroup.exists_isLeast_one_ltproof · cited by 2
- MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quotproof · cited by 2