Theorems · Theorem · linear algebra

TensorProduct.sum_tmul_basis_left_injective

∀ {R : Type u_1} {M : Type u_3} {N : Type u_4} {ι : Type u_5} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : AddCommMonoid N] [inst_4 : Module R N] (ℬ : Module.Basis ι R M),
  Function.Injective ⇑((Finsupp.lsum R) fun i => (TensorProduct.mk R M N) (ℬ i))

Defined in: Mathlib.LinearAlgebra.TensorProduct.Basis
Cited by: 0 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid Module AddCommMonoid Module

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DFunLike.coestatement · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement · cited by 10,215
Finsuppstatement · cited by 5,255
LinearEquivstatement · cited by 3,317
TensorProductstatement · cited by 2,545
Module.Basisstatement and proof · cited by 1,477
LinearEquiv.symmproof · cited by 1,461
LinearEquiv.injectiveproof · cited by 162

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