Theorems · Theorem · group theory
zero_zpow
∀ {G₀ : Type u_2} [inst : GroupWithZero G₀] (n : ℤ), n ≠ 0 → 0 ^ n = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- GroupWithZerostatement and proof · cited by 691
- zero_powproof · cited by 361
- zpow_natCastproof · cited by 271
- inv_zeroproof · cited by 184
- zpow_negSuccproof · cited by 92
Cited by19
Results whose statement or proof uses this declaration.
- MeromorphicNFAt.meromorphicOrderAt_eq_zero_iffproof · cited by 14
- zpow_add'proof · cited by 5
- zpow_eq_zero_iffproof · cited by 5
- meromorphicNFAt_toMeromorphicNFAtproof · cited by 5
- MeromorphicAt.meromorphicTrailingCoeffAt_zpowproof · cited by 5
- toMeromorphicNFAt_eq_selfproof · cited by 4
- meromorphicOrderAt_zpowproof · cited by 4
- deriv_zpowproof · cited by 4
- logDeriv_fun_zpowproof · cited by 4
- meromorphicOrderAt_add_eq_left_of_ltproof · cited by 3
- Complex.cpow_int_mulproof · cited by 3
- meromorphicNFAt_iff_analyticAt_orproof · cited by 3