tmul — Mathlib

English

If a₁ commutes with a₂ and b₁ commutes with b₂, then a₁ ⊗ b₁ commutes with a₂ ⊗ b₂.

Русский

Если a₁ commuting с a₂ и b₁ commuting с b₂, то a₁ ⊗ b₁ commuting с a₂ ⊗ b₂.

LaTeX

$$$ \text{Commute } a_1 a_2 \; \Rightarrow \; \text{Commute } b_1 b_2 \Rightarrow \text{Commute } (a_1 \otimes_R b_1) (a_2 \otimes_R b_2) $$$

Lean4

nonrec theorem _root_.Commute.tmul {a₁ a₂ : A} {b₁ b₂ : B} (ha : Commute a₁ a₂) (hb : Commute b₁ b₂) :
    Commute (a₁ ⊗ₜ[R] b₁) (a₂ ⊗ₜ[R] b₂) :=
  ha.tmul hb

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