Theorems · Theorem · commutative algebra

Algebra.FormallySmooth.lift.congr_simp

∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {B : Type u_1}
  [inst_3 : CommRing B] [inst_4 : Algebra R B] [inst_5 : Algebra.FormallySmooth R A] (I : Ideal B) (hI : IsNilpotent I)
  (g g_1 : A →ₐ[R] B ⧸ I), g = g_1 → Algebra.FormallySmooth.lift I hI g = Algebra.FormallySmooth.lift I hI g_1

Defined in

Mathlib.RingTheory.Smooth.Basic

Cited by

0 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebra.FormallySmooth