Theorems · Theorem · number theory
QuadraticMap.posDef_of_nonneg
∀ {M : Type u_4} {N : Type u_5} {R₂ : Type u} [inst : CommSemiring R₂] [inst_1 : AddCommMonoid M] [inst_2 : Module R₂ M]
[inst_3 : PartialOrder N] [inst_4 : AddCommMonoid N] [inst_5 : Module R₂ N] {Q : QuadraticMap R₂ M N},
(∀ (x : M), 0 ≤ Q x) → Q.Anisotropic → Q.PosDef- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- PartialOrderstatement and proof · cited by 6,410
- QuadraticMapstatement and proof · cited by 262
- lt_of_le_of_neproof · cited by 230
- QuadraticMap.PosDefstatement · cited by 31
- QuadraticMap.Anisotropicstatement and proof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- QuadraticMap.posDef_iff_nonnegproof · cited by 0