instNonUnitalNonAssocSemiring — Mathlib

English

Reiteration of the semiconjugacy lifting to tensors: tmul preserves semiconjugacy componentwise.

Русский

Повторное утверждение: преобразование через tmul сохраняет полусопряжённость по компонентам.

LaTeX

$$$ \text{SemiconjBy } a_1 a_2 a_3 \Rightarrow \text{SemiconjBy } b_1 b_2 b_3 \Rightarrow \text{SemiconjBy } (a_1 \otimes_R b_1) (a_2 \otimes_R b_2) (a_3 \otimes_R b_3) $$$

Lean4

instance instNonUnitalNonAssocSemiring : NonUnitalNonAssocSemiring (A ⊗[R] B)
    where
  left_distrib a b c := by simp [HMul.hMul, Mul.mul]
  right_distrib a b c := by simp [HMul.hMul, Mul.mul]
  zero_mul a := by simp [HMul.hMul, Mul.mul]
  mul_zero
    a := by
    simp [HMul.hMul, Mul.mul]
      -- we want `isScalarTower_right` to take priority since it's better for unification elsewhere

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