Documentation

Linglib.Core.Algebra.Group.WithOne

Finiteness and surjectivity for WithOne #

WithOne α is finite when α is, and WithOne.lift f is surjective exactly when 1 and the range of f cover the target.

instance WithOne.instFinite_linglib {α : Type u_1} [Finite α] :
Finite (WithOne α)
theorem WithOne.lift_surjective {α : Type u_1} {M : Type u_2} [Mul α] [MulOneClass M] {f : α →ₙ* M} :
Function.Surjective (lift f) ∀ (m : M), m = 1 m Set.range f