Theorems · Inductive type · group theory

DivisibleBy

(A : Type u_1) → (α : Type u_2) → [AddMonoid A] → [SMul α A] → [Zero α] → Type (max u_1 u_2)

An AddMonoid A is α-divisible iff n • x = a has a solution for all n ≠ 0 ∈ α and a ∈ A. Here we adopt a constructive approach where we ask an explicit div : A → α → A function such that * div a 0 = 0 for all a ∈ A * n • div a n = a for all n ≠ 0 ∈ α and a ∈ A.

Defined in

Mathlib.GroupTheory.Divisible

Cited by

8 results in Mathlib

Foundations

Depth 1 from the axioms · uses no axioms

Assumes

AddMonoidSMulZero