Theorems · Theorem · group theory
one_zpow
∀ {α : Type u_1} [inst : DivisionMonoid α] (n : ℤ), 1 ^ n = 1- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_powproof · cited by 521
- inv_oneproof · cited by 301
- zpow_natCastproof · cited by 271
- DivisionMonoidstatement and proof · cited by 201
- zpow_negSuccproof · cited by 92
Cited by44
Results whose statement or proof uses this declaration.
- Int.cast_negOnePowproof · cited by 10
- IsPrimitiveRoot.pow_of_coprimeproof · cited by 8
- ModularForm.SL_slash_applyproof · cited by 7
- zpow_mod_orderOfproof · cited by 6
- Complex.cpow_int_mulproof · cited by 3
- IsPrimitiveRoot.eq_pow_of_mem_rootsOfUnityproof · cited by 3
- zpow_pow_orderOfproof · cited by 2
- Subgroup.closure_singleton_oneproof · cited by 2
- hasFPowerSeriesAt_clog_oneproof · cited by 2
- zpow_eq_zpow_emodproof · cited by 2
- ModularForm.SL_slash_defproof · cited by 2