Theorems · Theorem · group theory
npow_add
∀ {M : Type u_1} [inst : MulOneClass M] [inst_1 : Pow M ℕ] [NatPowAssoc M] (k n : ℕ) (x : M),
x ^ (k + n) = x ^ k * x ^ n- Defined in
- Mathlib.Algebra.Group.NatPowAssoc
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- MulOneClassPowNatPowAssoc
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.
- MulOneClassstatement and proof · cited by 1,018
- NatPowAssocstatement and proof · cited by 53
- NatPowAssoc.npow_addproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.smeval_mul_Xproof · cited by 2
- Nat.cast_npowproof · cited by 1
- npow_mulproof · cited by 1
- Polynomial.smeval_monomial_mulproof · cited by 1
- Polynomial.smeval_X_mulproof · cited by 1
- Polynomial.smeval_at_zeroproof · cited by 0
- neg_npow_assocproof · cited by 0