Theorems · Theorem · group theory
DirectSum.decomposeLinearEquiv_symm_comp_lof
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} [inst : DecidableEq ι] [inst_1 : Semiring R] [inst_2 : AddCommMonoid M]
[inst_3 : Module R M] (ℳ : ι → Submodule R M) [inst_4 : DirectSum.Decomposition ℳ] (i : ι),
↑(DirectSum.decomposeLinearEquiv ℳ).symm ∘ₗ DirectSum.lof R ι (fun x => ↥(ℳ x)) i = (ℳ i).subtype- Defined in
- Mathlib.Algebra.DirectSum.Decomposition
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- LinearMap.compstatement · cited by 1,642
- LinearEquiv.symmstatement · cited by 1,461
- LinearEquiv.toLinearMapstatement · cited by 1,171
- LinearMap.extproof · cited by 844
- Submodule.subtypestatement · cited by 480
- DirectSumstatement · cited by 446
Cited by2
Results whose statement or proof uses this declaration.
- DirectSum.decomposeLinearEquiv_symm_lofproof · cited by 1
- DirectSum.decompose_lhom_extproof · cited by 0