Theorems · Theorem · group theory
DirectSum.decomposeLinearEquiv_apply_coe
∀ {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) (x : ↥(ℳ i)),
(DirectSum.decomposeLinearEquiv ℳ) ↑x = (DirectSum.lof R ι (fun i => ↥(ℳ i)) i) x- Defined in
- Mathlib.Algebra.DirectSum.Decomposition
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- LinearEquivstatement · cited by 3,317
- DirectSumstatement · cited by 446
- DirectSum.lofstatement · cited by 79
- DirectSum.Decompositionstatement and proof · cited by 57
- LinearEquiv.eq_symm_applyproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- DirectSum.decomposeLinearEquiv_comp_subtypeproof · cited by 1
- DirectSum.subtype_rTensor_injectiveproof · cited by 0