Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_monomial_ne
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {m n : σ →₀ ℕ},
m ≠ n → ∀ (a : R), (MvPowerSeries.coeff m) ((MvPowerSeries.monomial n) a) = 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement and proof · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement and proof · cited by 273
- Pi.single_eq_of_neproof · cited by 116
- MvPowerSeries.monomialstatement · cited by 69
- MvPowerSeries.monomial_defproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- MvPowerSeries.WithPiTopology.hasSum_of_monomials_selfproof · cited by 3
- MvPowerSeries.eq_of_coeff_monomial_ne_zeroproof · cited by 3
- MvPowerSeries.map_algebraMap_eq_subst_Xproof · cited by 1