Theorems · Theorem · commutative algebra

IsLocalizedModule.liftOfLE_apply

∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_2} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {M₁ : Type u_7}
  {M₂ : Type u_6} [inst_3 : AddCommMonoid M₁] [inst_4 : AddCommMonoid M₂] [inst_5 : Module R M₁] [inst_6 : Module R M₂]
  (S₁ S₂ : Submonoid R) (h : S₁ ≤ S₂) (f₁ : M →ₗ[R] M₁) (f₂ : M →ₗ[R] M₂) [inst_7 : IsLocalizedModule S₁ f₁]
  [inst_8 : IsLocalizedModule S₂ f₂] (x : M), (IsLocalizedModule.liftOfLE S₁ S₂ h f₁ f₂) (f₁ x) = f₂ x

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

0 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidAddCommMonoidModuleModuleIsLocalizedModuleIsLocalizedModule