Theorems · Theorem · linear algebra
TensorProduct.finsuppScalarLeft_apply_tmul
∀ {R : Type u_1} [inst : CommSemiring R] {N : Type u_4} [inst_1 : AddCommMonoid N] [inst_2 : Module R N] {ι : Type u_5}
[inst_3 : DecidableEq ι] (p : ι →₀ R) (n : N),
(TensorProduct.finsuppScalarLeft R N ι) (p ⊗ₜ[R] n) = p.sum fun i m => fun₀ | i => m • n- Defined in
- Mathlib.LinearAlgebra.DirectSum.Finsupp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- LinearEquivstatement · cited by 3,317
- TensorProductstatement · cited by 2,545
- TensorProduct.tmulstatement · cited by 1,182
- Finsupp.singlestatement and proof · cited by 943
- zero_smulproof · cited by 716
- Finsupp.sumstatement and proof · cited by 481
Cited by1
Results whose statement or proof uses this declaration.
- TensorProduct.vanishesTrivially_of_sum_tmul_eq_zeroproof · cited by 2