Theorems · Theorem · linear algebra

PiTensorProduct.tmulEquivDep_apply

∀ {ι : Type u_1} {ι₂ : Type u_2} (R : Type u_4) [inst : CommSemiring R] (N : ι ⊕ ι₂ → Type u_12)
  [inst_1 : (i : ι ⊕ ι₂) → AddCommMonoid (N i)] [inst_2 : (i : ι ⊕ ι₂) → Module R (N i)] (a : (i₁ : ι) → N (Sum.inl i₁))
  (b : (i₂ : ι₂) → N (Sum.inr i₂)),
  (PiTensorProduct.tmulEquivDep R N)
      (((PiTensorProduct.tprod R) fun i₁ => a i₁) ⊗ₜ[R] (PiTensorProduct.tprod R) fun i₂ => b i₂) =
    ⨂ₜ[R] (i : ι ⊕ ι₂), Sum.rec a b i

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.Basic

Cited by

1 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModule