Theorems · Theorem · order theory
Even.pow_nonneg
∀ {R : Type u_3} [inst : Semiring R] [inst_1 : LinearOrder R] [IsOrderedRing R] [ExistsAddOfLE R] {n : ℕ},
Even n → ∀ (a : R), 0 ≤ a ^ n- Defined in
- Mathlib.Algebra.Order.Ring.Basic
- Cited by
- 94 results in Mathlib
- Foundations
- Depth 19 from the axioms, rests on 225 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- IsOrderedRingstatement and proof · cited by 777
- Evenstatement and proof · cited by 444
- ExistsAddOfLEstatement and proof · cited by 330
- pow_addproof · cited by 315
- mul_self_nonnegproof · cited by 35
Cited by94
Results whose statement or proof uses this declaration.
- Orientation.oangle_selfproof · cited by 17
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- Even.pow_absproof · cited by 5
- hasFDerivAt_jacobiTheta₂proof · cited by 4
- AkraBazziRecurrence.eventually_bi_mul_le_rproof · cited by 4
- ProbabilityTheory.IsGaussian.memLp_idproof · cited by 4
- OrthonormalBasis.sum_sq_norm_inner_rightproof · cited by 3
- Complex.norm_exp_sub_one_sub_id_leproof · cited by 3
- ProbabilityTheory.gaussianReal_map_linearMapproof · cited by 3
- TemperedDistribution.besselPotential_besselPotential_applyproof · cited by 3
- SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adjproof · cited by 2