Theorems · Theorem · commutative algebra

DirectSum.decomposeLinearEquiv_comp_subtype

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (ℳ : ι → Submodule R M) [inst_3 : DecidableEq ι] [inst_4 : DirectSum.Decomposition ℳ] {i : ι},
  ↑(DirectSum.decomposeLinearEquiv ℳ) ∘ₗ (ℳ i).subtype = DirectSum.lof R ι (fun i => ↥(ℳ i)) i

Defined in

Mathlib.LinearAlgebra.TensorProduct.Decomposition

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleDecidableEqDirectSum.Decomposition