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⟩