Theorems · Theorem · commutative algebra

PolynomialModule.induction_linear

∀ {R : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {p : PolynomialModule R M → Prop} (x : PolynomialModule R M),
  p 0 →
    (∀ (x y : PolynomialModule R M), p x → p y → p (x + y)) →
      (∀ (n : ℕ) (m : M), p (PolynomialModule.single R n m)) → p x

Defined in

Mathlib.Algebra.Polynomial.Module.Basic

Cited by

6 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule