Theorems · Theorem · linear algebra

TensorPower.gradedMonoid_eq_of_cast

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {a b : GradedMonoid fun n => PiTensorProduct R fun x => M} (h : a.fst = b.fst),
  (TensorPower.cast R M h) a.snd = b.snd → a = b

Defined in: Mathlib.LinearAlgebra.TensorPower.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid Module

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Cites15

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 and proof · cited by 18,349
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
Equivproof · cited by 8,337
LinearEquivstatement and proof · cited by 3,317
PiTensorProductstatement and proof · cited by 181
finCongrproof · cited by 78
GradedMonoidstatement and proof · cited by 46
TensorPowerstatement and proof · cited by 40
PiTensorProduct.reindexproof · cited by 21

Cited by1

Results whose statement or proof uses this declaration.

TensorPower.list_prod_gradedMonoid_mk_singleproof · cited by 1