Theorems · Theorem · commutative algebra

MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSum

∀ (R : Type u_1) {M : Type u_2} [inst : CommSemiring R] {σ : Type u_3} [inst_1 : AddCommMonoid M] (w : σ → M)
  [inst_2 : DecidableEq σ] [inst_3 : DecidableEq R] [inst_4 : DecidableEq M]
  (x : DirectSum M fun i => ↥(MvPolynomial.weightedHomogeneousSubmodule R w i)),
  (DirectSum.coeLinearMap fun i => MvPolynomial.weightedHomogeneousSubmodule R w i) x = DFinsupp.sum x fun x x_1 => ↑x_1

Defined in: Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous
Cited by: 3 results in Mathlib
Foundations: Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid DecidableEq DecidableEq DecidableEq

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
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
Submodulestatement · cited by 7,192
Finsuppstatement · cited by 5,255
MvPolynomialstatement and proof · cited by 2,140
DirectSumstatement and proof · cited by 446
DFinsupp.sumstatement and proof · cited by 64
MvPolynomial.weightedHomogeneousSubmodulestatement and proof · cited by 23
DirectSum.coeLinearMapstatement · cited by 15

Cited by3

Results whose statement or proof uses this declaration.

MvPolynomial.DirectSum.coeLinearMap_eq_finsumproof · cited by 0
MvPolynomial.weightedHomogeneousComponent_directSumproof · cited by 0
MvPolynomial.DirectSum.coeAddMonoidHom_eq_support_sumproof · cited by 0