isSMulRegular_iff — Mathlib

English

IsSMulRegular (R × S) r holds iff IsSMulRegular R r and IsSMulRegular S r.

Русский

IsSMulRegular на произведении R × S через r эквивалентно IsSMulRegular на каждом из факторов.

LaTeX

$$IsSMulRegular (Prod R S) r \iff IsSMulRegular R r ∧ IsSMulRegular S r$$

Lean4

@[simp]
theorem isSMulRegular_iff [SMul α R] [SMul α S] {r : α} [Nonempty R] [Nonempty S] :
    IsSMulRegular (R × S) r ↔ IsSMulRegular R r ∧ IsSMulRegular S r :=
  Prod.map_injective

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