Documentation

Mathlib.Algebra.Module.Pi

Pi instances for modules #

This file defines instances for module and related structures on Pi Types

theorem IsSMulRegular.pi {I : Type u} {f : IType v} {α : Type u_1} [(i : I) → SMul α (f i)] {k : α} (hk : ∀ (i : I), IsSMulRegular (f i) k) :
IsSMulRegular ((i : I) → f i) k
instance Pi.module (I : Type u) (f : IType v) (α : Type u_1) {r : Semiring α} {m : (i : I) → AddCommMonoid (f i)} [(i : I) → Module α (f i)] :
Module α ((i : I) → f i)
Equations
instance Pi.Function.module (I : Type u) (α : Type u_1) (β : Type u_2) [Semiring α] [AddCommMonoid β] [Module α β] :
Module α (Iβ)

A special case of Pi.module for non-dependent types. Lean struggles to elaborate definitions elsewhere in the library without this.

Equations
instance Pi.module' {I : Type u} {f : IType v} {g : IType u_1} {r : (i : I) → Semiring (f i)} {m : (i : I) → AddCommMonoid (g i)} [(i : I) → Module (f i) (g i)] :
Module ((i : I) → f i) ((i : I) → g i)
Equations