Theorems · Theorem · linear algebra
TensorProduct.finsuppScalarLeft_symm_apply_single
∀ {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] (i : ι) (n : N),
((TensorProduct.finsuppScalarLeft R N ι).symm fun₀ | i => n) = (fun₀ | i => 1) ⊗ₜ[R] n- Defined in
- Mathlib.LinearAlgebra.DirectSum.Finsupp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 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 · cited by 5,255
- LinearEquivstatement · cited by 3,317
- TensorProductstatement · cited by 2,545
- LinearEquiv.symmstatement and proof · cited by 1,461
- TensorProduct.tmulstatement and proof · cited by 1,182
- Finsupp.singlestatement and proof · cited by 943
- TensorProduct.lidproof · cited by 96
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.mulLeftMap_eq_mulMap_compproof · cited by 2