Theorems · Theorem · group theory

DirectSum.AddSubmonoidClass.IsHomogeneous.ext

∀ {ι : Type u_1} {M : Type u_3} {σ : Type u_4} [inst : DecidableEq ι] [inst_1 : AddCommMonoid M] [inst_2 : SetLike σ M]
  [inst_3 : AddSubmonoidClass σ M] {ℳ : ι → σ} [inst_4 : DirectSum.Decomposition ℳ] {P : Type u_5}
  [inst_5 : SetLike P M] [AddSubmonoidClass P M] {p q : P},
  DirectSum.SetLike.IsHomogeneous ℳ p →
    DirectSum.SetLike.IsHomogeneous ℳ q → (∀ (i : ι), ∀ m ∈ ℳ i, m ∈ p ↔ m ∈ q) → p = q

Defined in

Mathlib.Algebra.DirectSum.Decomposition

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCommMonoidSetLikeAddSubmonoidClassDirectSum.DecompositionSetLikeAddSubmonoidClass