Theorems · Theorem · group theory
pow_add
∀ {M : Type u_2} [inst : Monoid M] (a : M) (m n : ℕ), a ^ (m + n) = a ^ m * a ^ n- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 315 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 58 definitions · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by315
Results whose statement or proof uses this declaration.
- Even.pow_nonnegproof · cited by 94
- pow_dvd_powproof · cited by 56
- Ideal.radical_eq_sInfproof · cited by 21
- Finset.prod_pow_eq_pow_sumproof · cited by 18
- Odd.neg_powproof · cited by 14
- MeromorphicAt.smulproof · cited by 13
- pow_mod_orderOfproof · cited by 12
- pow_sub₀proof · cited by 9
- Equiv.Perm.sign_of_cycleTypeproof · cited by 7
- Module.End.pow_map_zero_of_leproof · cited by 6
- Matrix.det_succ_rowproof · cited by 6
- Complex.exp_boundproof · cited by 6
Showing the 200 most cited of 315.