Theorems · Theorem · commutative algebra

Module.Basis.ofIsLocalizedModule.congr_simp

∀ {R : Type u_1} (Rₛ : Type u_2) [inst : CommSemiring R] (S S_1 : Submonoid R) (e_S : S = S_1)
  [inst_1 : CommSemiring Rₛ] [inst_2 : Algebra R Rₛ] [inst_3 : IsLocalization S Rₛ] {M : Type u_3} {Mₛ : Type u_4}
  [inst_4 : AddCommMonoid M] [inst_5 : Module R M] [inst_6 : AddCommMonoid Mₛ] [inst_7 : Module R Mₛ]
  [inst_8 : Module Rₛ Mₛ] [inst_9 : IsScalarTower R Rₛ Mₛ] (f f_1 : M →ₗ[R] Mₛ) (e_f : f = f_1)
  [inst_10 : IsLocalizedModule S f] {ι : Type u_5} (b b_1 : Module.Basis ι R M),
  b = b_1 → Module.Basis.ofIsLocalizedModule Rₛ S f b = Module.Basis.ofIsLocalizedModule Rₛ S_1 f_1 b_1

Defined in

Mathlib.RingTheory.Localization.Module

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraIsLocalizationAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerIsLocalizedModule