Theorems · Theorem · commutative algebra

DividedPowerAlgebra.induction_on

∀ {R : Type u_2} {M : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {P : DividedPowerAlgebra R M → Prop} (f : DividedPowerAlgebra R M),
  (∀ (a : R), P ((algebraMap R (DividedPowerAlgebra R M)) a)) →
    (∀ (f g : DividedPowerAlgebra R M), P f → P g → P (f + g)) →
      (∀ (f : DividedPowerAlgebra R M) (n : ℕ) (m : M), P f → P (f * DividedPowerAlgebra.dp R n m)) → P f

Defined in

Mathlib.RingTheory.DividedPowerAlgebra.Init

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModule