Theorems · Theorem · linear algebra
PiTensorProduct.liftAux.smul
∀ {ι : Type u_1} {R : Type u_4} [inst : CommSemiring R] {s : ι → Type u_7} [inst_1 : (i : ι) → AddCommMonoid (s i)]
[inst_2 : (i : ι) → Module R (s i)] {E : Type u_9} [inst_3 : AddCommMonoid E] [inst_4 : Module R E]
{φ : MultilinearMap R s E} (r : R) (x : PiTensorProduct R fun i => s i),
(PiTensorProduct.liftAux φ) (r • x) = r • (PiTensorProduct.liftAux φ) x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- AddMonoidHomstatement · cited by 3,230
- MultilinearMapstatement and proof · cited by 370
- smul_addproof · cited by 263
- PiTensorProductstatement and proof · cited by 181
- smul_assocproof · cited by 150
- AddMonoidHom.map_addproof · cited by 48
- PiTensorProduct.tprodCoeffproof · cited by 13
- PiTensorProduct.liftAuxstatement and proof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- PiTensorProduct.liftproof · cited by 30