Theorems · Theorem · linear algebra
MultilinearMap.mkPiRing_apply_one_eq_self
∀ {R : Type uR} {ι : Type uι} {M₂ : Type v₂} [inst : CommSemiring R] [inst_1 : AddCommMonoid M₂] [inst_2 : Module R M₂]
[inst_3 : Fintype ι] (f : MultilinearMap R (fun x => R) M₂), MultilinearMap.mkPiRing R ι (f fun x => 1) = f- Defined in
- Mathlib.LinearAlgebra.Multilinear.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- one_smulproof · cited by 1,374
- MultilinearMapstatement and proof · cited by 370
- Finset.prod_const_oneproof · cited by 100
- MultilinearMap.mkPiRingstatement · cited by 8
- MultilinearMap.ext_ringproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- MultilinearMap.freeDFinsuppEquiv_singleproof · cited by 2
- ContinuousMultilinearMap.mkPiRing_apply_one_eq_selfproof · cited by 2
- MultilinearMap.piRingEquivproof · cited by 1