Theorems · Theorem · order theory
neg_neg_of_pos
∀ {α : Type u} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] {a : α}, 0 < a → -a < 0- Defined in
- Mathlib.Algebra.Order.Group.Defs
- Cited by
- 227 results in Mathlib
- Foundations
- Depth 16 from the axioms, rests on 96 definitions · uses propext
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.
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- neg_neg_iff_posproof · cited by 2
Cited by227
Results whose statement or proof uses this declaration.
- Complex.Gamma_add_oneproof · cited by 12
- AnalyticAt.zpowproof · cited by 8
- Field.finSepDegree_eq_finrank_of_isSeparableproof · cited by 7
- Chebyshev.psi_eq_zero_of_lt_twoproof · cited by 7
- Chebyshev.theta_eq_zero_of_lt_twoproof · cited by 6
- Real.cos_pi_div_threeproof · cited by 5
- PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExceptproof · cited by 4
- TendstoLocallyUniformlyOn.smul₀_of_isBoundedUnderproof · cited by 4
- NumberField.hermiteTheorem.rank_le_rankOfDiscrBddproof · cited by 4
- Real.binEntropy_neg_of_negproof · cited by 4
- Function.locallyFinsuppWithin.logCounting_nonnegproof · cited by 3
- Integrable.norm_condExp_rpow_leproof · cited by 3
Showing the 200 most cited of 227.