Theorems · Theorem · linear algebra
Submodule.set_smul_eq_map
∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (sR : Set R)
(N : Submodule R M) [inst_3 : SMulCommClass R R ↥N],
sR • N = Submodule.map (N.subtype ∘ₗ (Finsupp.lsum R) (DistribSMul.toLinearMap R ↥N)) (Finsupp.supported (↥N) R sR)- Defined in
- Mathlib.Algebra.Module.Submodule.Finsupp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- 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
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.ofPredproof · cited by 6,101
- Finsuppstatement and proof · cited by 5,255
- LinearEquivstatement · cited by 3,317
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.mem_set_smulproof · cited by 1