Theorems · Theorem · linear algebra

PiTensorProduct.smul_tprodCoeff

∀ {ι : Type u_1} {R : Type u_4} [inst : CommSemiring R] {R₁ : Type u_5} {s : ι → Type u_7}
  [inst_1 : (i : ι) → AddCommMonoid (s i)] [inst_2 : (i : ι) → Module R (s i)] [inst_3 : DecidableEq ι] (z : R)
  (f : (i : ι) → s i) (i : ι) (r : R₁) [inst_4 : SMul R₁ R] [IsScalarTower R₁ R R] [inst_6 : SMul R₁ (s i)]
  [IsScalarTower R₁ R (s i)],
  PiTensorProduct.tprodCoeff R z (Function.update f i (r • f i)) = PiTensorProduct.tprodCoeff R (r • z) f

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.Basic

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleDecidableEqSMulIsScalarTowerSMulIsScalarTower