Theorems · Theorem · order theory
Odd.pos
∀ {R : Type u} [inst : Semiring R] [inst_1 : PartialOrder R] [CanonicallyOrderedAdd R] [Nontrivial R] {a : R},
Odd a → 0 < a- Defined in
- Mathlib.Algebra.Order.Ring.Canonical
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- Nontrivialstatement and proof · cited by 2,416
- Oddstatement and proof · cited by 364
- CanonicallyOrderedAddstatement and proof · cited by 229
Cited by9
Results whose statement or proof uses this declaration.
- jacobiSym.value_atproof · cited by 4
- Polynomial.Chebyshev.isLocalMin_T_realproof · cited by 1
- SimpleGraph.IsTutteViolator.emptyproof · cited by 1
- Polynomial.coeff_hermite_of_odd_addproof · cited by 1
- DihedralGroup.card_commute_oddproof · cited by 1
- DihedralGroup.card_conjClasses_oddproof · cited by 1
- padicValNat.pow_add_powproof · cited by 0
- DihedralGroup.commProb_reciprocalproof · cited by 0
- IsPrimitiveRoot.pow_add_pow_eq_prod_add_mulproof · cited by 0