Theorems · Theorem · group theory
pow_succ
∀ {M : Type u_2} [inst : Monoid M] (a : M) (n : ℕ), a ^ (n + 1) = a ^ n * a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 374 results in Mathlib
- Foundations
- Depth 9 from the axioms, rests on 49 definitions · uses no axioms
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- Monoid.npow_succproof · cited by 1
Cited by374
Results whose statement or proof uses this declaration.
- pow_oneproof · cited by 894
- zero_powproof · cited by 361
- pow_twoproof · cited by 150
- Complex.ofReal_powproof · cited by 81
- Int.cast_powproof · cited by 59
- Complex.exp_zeroproof · cited by 43
- Real.log_powproof · cited by 29
- pow_right_mono₀proof · cited by 19
- tendsto_pow_atTop_nhds_zero_of_lt_oneproof · cited by 18
- zpow_add_oneproof · cited by 18
- Polynomial.map_compproof · cited by 14
- Polynomial.X_pow_mulproof · cited by 12
Showing the 200 most cited of 374.