Theorems · Theorem · group theory
pow_zero
∀ {M : Type u_2} [inst : Monoid M] (a : M), a ^ 0 = 1- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 1,094 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 34 definitions · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- Monoid.npow_zeroproof · cited by 1
Cited by1,094
Results whose statement or proof uses this declaration.
- pow_oneproof · cited by 894
- zpow_negproof · cited by 198
- Complex.ofReal_powproof · cited by 81
- Int.cast_powproof · cited by 59
- Polynomial.eval₂_Cproof · cited by 50
- Complex.exp_zeroproof · cited by 43
- zpow_addproof · cited by 40
- MvPolynomial.eval₂_Xproof · cited by 36
- Polynomial.derivative_Cproof · cited by 30
- zpow_add₀proof · cited by 30
- List.prod_replicateproof · cited by 29
- Real.log_powproof · cited by 29
Showing the 200 most cited of 1,094.