Theorems · Theorem · linear algebra

TensorProduct.AlgebraTensorModule.curry_injective

∀ {R : Type uR} {A : Type uA} {M : Type uM} {N : Type uN} {P : Type uP} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Algebra R A] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module A M]
  [inst_6 : IsScalarTower R A M] [inst_7 : AddCommMonoid N] [inst_8 : Module R N] [inst_9 : AddCommMonoid P]
  [inst_10 : Module R P] [inst_11 : Module A P] [inst_12 : IsScalarTower R A P],
  Function.Injective TensorProduct.AlgebraTensorModule.curry

Just as TensorProduct.ext is marked ext instead of TensorProduct.ext', this is a better ext lemma than TensorProduct.AlgebraTensorModule.ext below. See note [partially-applied ext lemmas].

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

159 results in Mathlib

Foundations

Depth 70 from the axioms, rests on 941 definitions · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTower