Theorems · Theorem · group theory
zero_pow_eq
∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] (n : ℕ), 0 ^ n = if n = 0 then 1 else 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- MonoidWithZero
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.
- pow_zeroproof · cited by 1,094
- MonoidWithZerostatement and proof · cited by 456
- zero_powproof · cited by 361
Cited by10
Results whose statement or proof uses this declaration.
- Height.max_mulHeightBound_zero_one_eq_oneproof · cited by 2
- PowerSeries.subst_substInv_rightproof · cited by 2
- IsPrimitiveRoot.zeroproof · cited by 2
- Polynomial.scaleRoots_zeroproof · cited by 2
- PowerSeries.coeff_subst_sum_C_substInvFun_mul_X_pow_sub_Xproof · cited by 1
- AlgHom.IsArithFrobAt.le_comapproof · cited by 1
- Polynomial.eval₂_at_zeroproof · cited by 1
- Polynomial.pow_scaleRoots_of_isReducedproof · cited by 0
- zero_pow_eq_one₀proof · cited by 0
- Nat.pow_sub_one_mod_pow_sub_oneproof · cited by 0