Theorems · Theorem · commutative algebra

Submodule.fg_induction

∀ {R : Type u_4} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {motive : (N : Submodule R M) → N.FG → Prop},
  (∀ (x : M), motive (R ∙ x) ⋯) →
    (∀ (N₁ N₂ : Submodule R M) (hN₁ : N₁.FG) (hN₂ : N₂.FG), motive N₁ hN₁ → motive N₂ hN₂ → motive (N₁ ⊔ N₂) ⋯) →
      ∀ (N : Submodule R M) (hN : N.FG), motive N hN

Defined in

Mathlib.RingTheory.Finiteness.Basic

Cited by

3 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule