Theorems · Theorem · commutative algebra

Submodule.fg_sup_span_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},
  motive ⊥ ⋯ →
    (∀ (N : Submodule R M) (x : M) (hN : N.FG), motive N hN → motive (N ⊔ R ∙ x) ⋯) →
      ∀ (N : Submodule R M) (hN : N.FG), motive N hN

Defined in

Mathlib.RingTheory.Finiteness.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModule