Theorems · Theorem · group theory

DirectSum.Decomposition.inductionOn

∀ {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) [DirectSum.Decomposition ℳ] {motive : M → Prop},
  motive 0 →
    (∀ {i : ι} (m : ↥(ℳ i)), motive ↑m) → (∀ (m m' : M), motive m → motive m' → motive (m + m')) → ∀ (m : M), motive m

Defined in

Mathlib.Algebra.DirectSum.Decomposition

Cited by

2 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCommMonoidSetLikeAddSubmonoidClassDirectSum.Decomposition