Theorems · Theorem · number theory

QuadraticForm.tmul_comp_tensorAssoc

∀ {R : Type uR} {M₁ : Type uM₁} {M₂ : Type uM₂} {M₃ : Type uM₃} [inst : CommRing R] [inst_1 : AddCommGroup M₁]
  [inst_2 : AddCommGroup M₂] [inst_3 : AddCommGroup M₃] [inst_4 : Module R M₁] [inst_5 : Module R M₂]
  [inst_6 : Module R M₃] [inst_7 : Invertible 2] (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂)
  (Q₃ : QuadraticForm R M₃),
  QuadraticMap.comp (Q₁.tmul (Q₂.tmul Q₃)) ↑(TensorProduct.assoc R M₁ M₂ M₃) = (Q₁.tmul Q₂).tmul Q₃

Defined in

Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupAddCommGroupModuleModuleModuleInvertible