instDistribMulActionQuotientOfIsScalarTower

English

The coercion commutes with iInf: the coercion of the infimum is the infimum of the coerced elements.

Русский

Приведение к элементу соглашается с инф-инфом: приведение iInf f равняется Inf коe(f i).

LaTeX

$$$\\iInf f$ coerces to $\\iInf_{i} f(i)$, i.e. $\\uparrow(\\iInf f) = \\iInf i\\, (\\uparrow f(i))$$$

Lean4

instance [Monoid α] [NonAssocSemiring R] [DistribMulAction α R] [IsScalarTower α R R] (c : RingCon R) :
    DistribMulAction α c.Quotient :=
  { c.toCon.mulAction with
    smul_zero := fun _ => congr_arg toQuotient <| smul_zero _
    smul_add := fun _ => Quotient.ind₂' fun _ _ => congr_arg toQuotient <| smul_add _ _ _ }

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