Theorems · Theorem · number theory

le_sigNeg_of_negDef

∀ {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] {V : Submodule R M},
  (QuadraticMap.restrict (-Q) V).PosDef → Module.finrank R ↥V ≤ sigNeg Q

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Signature

Cited by

0 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupCommRingLinearOrderModuleModule.FiniteStrongRankCondition