Theorems · Theorem · number theory
QuadraticForm.polarBilin_tmul
∀ {R : Type uR} {A : Type uA} {M₁ : Type uM₁} {M₂ : Type uM₂} [inst : CommRing R] [inst_1 : CommRing A]
[inst_2 : AddCommGroup M₁] [inst_3 : AddCommGroup M₂] [inst_4 : Algebra R A] [inst_5 : Module R M₁]
[inst_6 : Module A M₁] [inst_7 : SMulCommClass R A M₁] [inst_8 : IsScalarTower R A M₁] [inst_9 : Module R M₂]
[inst_10 : Invertible 2] [inst_11 : Invertible 2] (Q₁ : QuadraticForm A M₁) (Q₂ : QuadraticForm R M₂),
QuadraticMap.polarBilin (Q₁.tmul Q₂) =
⅟2 • LinearMap.BilinForm.tmul (QuadraticMap.polarBilin Q₁) (QuadraticMap.polarBilin Q₂)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- IsScalarTowerstatement and proof · cited by 3,896
- TensorProductstatement and proof · cited by 2,545
- SMulCommClassstatement and proof · cited by 1,927
- one_smulproof · cited by 1,374
- TensorProduct.tmulproof · cited by 1,182
Cited by1
Results whose statement or proof uses this declaration.
- QuadraticForm.polarBilin_baseChangeproof · cited by 0