Theorems · Theorem · linear algebra
TensorProduct.finsuppScalarLeft_apply
∀ {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] (pn : TensorProduct R (ι →₀ R) N) (i : ι),
((TensorProduct.finsuppScalarLeft R N ι) pn) i = (TensorProduct.lid R N) ((LinearMap.rTensor N (Finsupp.lapply i)) pn)- Defined in
- Mathlib.LinearAlgebra.DirectSum.Finsupp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
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
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- LinearEquivstatement · cited by 3,317
- TensorProductstatement and proof · cited by 2,545
- LinearMap.rTensorstatement and proof · cited by 266
- TensorProduct.lidstatement and proof · cited by 96
- Finsupp.lapplystatement and proof · cited by 19
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