Theorems · Theorem · order theory
pow_nonneg
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : Preorder M₀] {a : M₀} [ZeroLEOneClass M₀] [PosMulMono M₀],
0 ≤ a → ∀ (n : ℕ), 0 ≤ a ^ n- Cited by
- 141 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 75 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- MonoidWithZerostatement and proof · cited by 456
- ZeroLEOneClassstatement and proof · cited by 304
- PosMulMonostatement and proof · cited by 165
Cited by141
Results whose statement or proof uses this declaration.
- pow_right_mono₀proof · cited by 19
- hasSum_geometric_of_lt_oneproof · cited by 14
- zpow_nonnegproof · cited by 7
- Complex.exp_boundproof · cited by 6
- HurwitzKernelBounds.summable_f_natproof · cited by 5
- FormalMultilinearSeries.summable_norm_mul_powproof · cited by 5
- Real.pi_upper_bound_startproof · cited by 5
- Real.sum_le_exp_of_nonnegproof · cited by 5
- PeriodPair.hasSumLocallyUniformly_weierstrassPExceptproof · cited by 4
- Complex.norm_log_sub_logTaylor_leproof · cited by 4
- Real.abs_log_sub_add_sum_range_leproof · cited by 4
- Real.ofDigitsTerm_nonnegproof · cited by 4