Theorems · Theorem · number theory
QuadraticMap.posDef_pi_iff
∀ {ι : Type u_1} {R : Type u_2} {Mᵢ : ι → Type u_8} [inst : CommSemiring R] [inst_1 : (i : ι) → AddCommMonoid (Mᵢ i)]
[inst_2 : (i : ι) → Module R (Mᵢ i)] {P : Type u_10} [inst_3 : Fintype ι] [inst_4 : AddCommMonoid P]
[inst_5 : PartialOrder P] [IsOrderedAddMonoid P] [inst_7 : Module R P] {Q : (i : ι) → QuadraticMap R (Mᵢ i) P},
(QuadraticMap.pi Q).PosDef ↔ ∀ (i : ι), (Q i).PosDef- Defined in
- Mathlib.LinearAlgebra.QuadraticForm.Prod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Finset.univproof · cited by 3,473
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Finset.mem_univproof · cited by 361
- QuadraticMapstatement and proof · cited by 262
- QuadraticMap.PosDefstatement · cited by 31
- Finset.sum_eq_zero_iff_of_nonnegproof · cited by 19
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