Theorems · Theorem · commutative algebra
TensorProduct.smul_add
∀ {R : Type u_1} {R' : Type u_4} [inst : CommSemiring R] [inst_1 : Monoid R'] {M : Type u_7} {N : Type u_8}
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N] [inst_4 : DistribMulAction R' M] [inst_5 : Module R M]
[inst_6 : Module R N] [inst_7 : SMulCommClass R R' M] (r : R') (x y : TensorProduct R M N),
r • (x + y) = r • x + r • y- Defined in
- Mathlib.LinearAlgebra.TensorProduct.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Monoidstatement and proof · cited by 3,887
- TensorProductstatement and proof · cited by 2,545
- SMulCommClassstatement and proof · cited by 1,927
- map_addproof · cited by 964
- DistribMulActionstatement and proof · cited by 584
- addConGenproof · cited by 28
- AddCon.liftproof · cited by 14
- TensorProduct.Eqvproof · cited by 8
- TensorProduct.SMul.auxproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- TensorProduct.one_smulproof · cited by 0
- TensorProduct.zero_smulproof · cited by 0
- TensorProduct.add_smulproof · cited by 0