Theorems · Theorem · commutative algebra

IsAdicComplete.lift.congr_simp

∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {N : Type u_5} [inst_3 : AddCommGroup N] [inst_4 : Module R N] [inst_5 : IsAdicComplete I N]
  (f f_1 : (n : ℕ) → M →ₗ[R] N ⧸ I ^ n • ⊤) (e_f : f = f_1)
  (h : ∀ {m n : ℕ} (hle : m ≤ n), Submodule.factorPow I N hle ∘ₗ f n = f m),
  IsAdicComplete.lift I f h = IsAdicComplete.lift I f_1 ⋯

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

0 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleIsAdicComplete