Theorems · Theorem · commutative algebra
TensorProduct.smul_tmul_smul
∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_7} {N : Type u_8} [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] (r s : R) (m : M) (n : N),
(r • m) ⊗ₜ[R] (s • n) = (r * s) • m ⊗ₜ[R] n- Defined in
- Mathlib.LinearAlgebra.TensorProduct.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- TensorProductstatement · cited by 2,545
- TensorProduct.tmulstatement and proof · cited by 1,182
- SemigroupAction.mul_smulproof · cited by 291
- TensorProduct.smul_tmulproof · cited by 33
- TensorProduct.tmul_smulproof · cited by 33
Cited by1
Results whose statement or proof uses this declaration.
- InnerProductSpace.canonicalCovariantTensor_eq_sumproof · cited by 3