smul_iff — Mathlib

English

If a and b are right-regular, then the pair (a,b) is right-regular.

Русский

Если a и b прав-регулярны, то пара (a,b) прав-регулярна.

LaTeX

$$IsRightRegular a ∧ IsRightRegular b → IsRightRegular { fst := a, snd := b }$$

Lean4

/-- An element is `M`-regular if and only if multiplying it on the left by an `M`-regular element
is `M`-regular. -/
@[simp]
theorem smul_iff (b : S) (ha : IsSMulRegular M a) : IsSMulRegular M (a • b) ↔ IsSMulRegular M b :=
  ⟨of_smul _, ha.smul⟩

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