Theorems · Theorem · commutative algebra

AdicCompletion.induction_on

∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (M : Type u_4) [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {p : AdicCompletion I M → Prop} (x : AdicCompletion I M),
  (∀ (f : AdicCompletion.AdicCauchySequence I M), p ((AdicCompletion.mk I M) f)) → p x

To show a statement about an element of adicCompletion I M, it suffices to check it on Cauchy sequences.

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

9 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule