Theorems · Theorem · number theory
sigNeg_isGreatest
∀ {R : Type u_1} {M : Type u_2} [inst : AddCommGroup M] [inst_1 : CommRing R] [inst_2 : LinearOrder R]
[inst_3 : Module R M] (Q : QuadraticForm R M) [Module.Finite R M] [StrongRankCondition R],
IsGreatest {r | ∃ V, Module.finrank R ↥V = r ∧ (QuadraticMap.restrict (-Q) V).PosDef} (sigNeg Q)Defining property of sigNeg.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Submodulestatement · cited by 7,192
- Set.ofPredstatement · cited by 6,101
- Module.finrankstatement · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
- QuadraticFormstatement and proof · cited by 507
- StrongRankConditionstatement and proof · cited by 286
- IsGreateststatement · cited by 112
- QuadraticMap.PosDefstatement · cited by 31
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