Theorems · Theorem · number theory
QuadraticMap.PosDef.le_zero_iff
∀ {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},
Q.PosDef → ∀ {x : M}, Q x ≤ 0 ↔ x = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- le_antisymmproof · cited by 2,068
- map_zeroproof · cited by 1,614
- QuadraticMapstatement and proof · cited by 262
- QuadraticMap.PosDefstatement and proof · cited by 31
- QuadraticMap.PosDef.anisotropicproof · cited by 2
- QuadraticMap.PosDef.nonnegproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.linearIndependent_of_pairwise_le_zeroproof · cited by 1