Theorems · Theorem · group theory
zero_pow
∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] {n : ℕ}, n ≠ 0 → 0 ^ n = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 361 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 72 definitions · 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.
- MulZeroClass.mul_zeroproof · cited by 2,091
- MonoidWithZerostatement and proof · cited by 456
- pow_succproof · cited by 374
Cited by361
Results whose statement or proof uses this declaration.
- Real.log_powproof · cited by 29
- Polynomial.coeff_zero_eq_eval_zeroproof · cited by 20
- zero_zpowproof · cited by 19
- Nat.factorization_powproof · cited by 17
- Real.arctan_zeroproof · cited by 17
- pow_eq_zero_iffproof · cited by 16
- MeasureTheory.Measure.addHaar_smulproof · cited by 13
- MeromorphicAt.congrproof · cited by 12
- Polynomial.natDegree_powproof · cited by 11
- zero_pow_eqproof · cited by 10
- ENNReal.inv_powproof · cited by 9
- MeromorphicAt.invproof · cited by 9
Showing the 200 most cited of 361.