Theorems · Theorem · linear algebra

Submodule.linearMap_qext

∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (p : Submodule R M)
  {R₂ : Type u_3} {M₂ : Type u_4} [inst_3 : Ring R₂] [inst_4 : AddCommGroup M₂] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
  ⦃f g : M ⧸ p →ₛₗ[τ₁₂] M₂⦄, f ∘ₛₗ p.mkQ = g ∘ₛₗ p.mkQ → f = g

Two LinearMaps from a quotient module are equal if their compositions with submodule.mkQ are equal. See note [partially-applied ext lemmas].

Defined in

Mathlib.LinearAlgebra.Quotient.Defs

Cited by

13 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleRingAddCommGroupModule