Theorems · Theorem · linear algebra

TensorProduct.ext

∀ {R : Type u_1} {R₂ : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring R₂] {σ₁₂ : R →+* R₂} {M : Type u_7}
  {N : Type u_8} {P₂ : Type u_17} [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N] [inst_4 : AddCommMonoid P₂]
  [inst_5 : Module R M] [inst_6 : Module R N] [inst_7 : Module R₂ P₂] {g h : TensorProduct R M N →ₛₗ[σ₁₂] P₂},
  (TensorProduct.mk R M N).compr₂ₛₗ g = (TensorProduct.mk R M N).compr₂ₛₗ h → g = h

This used to be an @[ext] lemma, but it fails very slowly when the ext tactic tries to apply it in some cases, notably when one wants to show equality of two linear maps. The @[ext] attribute is now added locally where it is needed. Using this as the @[ext] lemma instead of TensorProduct.ext' allows ext to apply lemmas specific to M →ₗ _ and N →ₗ _. See note [partially-applied ext lemmas].

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basic

Cited by

50 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule