Theorems · Definition · order theory

MvPowerSeries.lexOrder

{σ : Type u_1} →
  {R : Type u_2} →
    [Semiring R] → [inst : LinearOrder σ] → [WellFoundedGT σ] → MvPowerSeries σ R → WithTop (Lex (σ →₀ ℕ))

The lex order on multivariate power series.

Defined in: Mathlib.RingTheory.MvPowerSeries.LexOrder
Cited by: 14 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring LinearOrder WellFoundedGT

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites15

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

DFunLike.coeproof · cited by 62,936
Semiringstatement and proof · cited by 13,802
Top.topproof · cited by 9,680
LinearOrderstatement and proof · cited by 8,572
Set.imageproof · cited by 5,609
Finsuppstatement · cited by 5,255
WithTopstatement · cited by 3,754
Set.Nonemptyproof · cited by 2,627
WithTop.someproof · cited by 1,128
MvPowerSeriesstatement and proof · cited by 659
Function.supportproof · cited by 610
Lexstatement · cited by 370

Cited by14

Results whose statement or proof uses this declaration.

MvPowerSeries.coeff_eq_zero_of_lt_lexOrderstatement and proof · cited by 5
MvPowerSeries.exists_finsupp_eq_lexOrder_of_ne_zerostatement and proof · cited by 2
MvPowerSeries.le_lexOrder_iffstatement and proof · cited by 2
MvPowerSeries.coeff_ne_zero_of_lexOrderstatement and proof · cited by 2
MvPowerSeries.lexOrder_def_of_ne_zerostatement · cited by 2
MvPowerSeries.lexOrder_mul_gestatement · cited by 1
MvPowerSeries.lexOrder_zerostatement · cited by 1
MvPowerSeries.lexOrder.congr_simpstatement and proof · cited by 1
MvPowerSeries.coeff_mul_of_add_lexOrderstatement and proof · cited by 1
MvPowerSeries.le_lexOrder_mulstatement and proof · cited by 1
MvPowerSeries.lexOrder_eq_top_iff_eq_zerostatement · cited by 1
MvPowerSeries.lexOrder_le_of_coeff_ne_zerostatement and proof · cited by 1