Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_zero_eq_constantCoeff
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R], ⇑(MvPowerSeries.coeff 0) = ⇑MvPowerSeries.constantCoeff- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 94 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.
Cites9
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
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- MvPowerSeriesstatement · cited by 659
- MvPowerSeries.coeffstatement · cited by 273
- MvPowerSeries.constantCoeffstatement · cited by 98
Cited by6
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_eq_zero_of_constantCoeff_nilpotentproof · cited by 2
- PowerSeries.HasSubst.monomialproof · cited by 1
- MvPowerSeries.mem_nonZeroDivisorsLeft_of_constantCoeffproof · cited by 1
- MvPowerSeries.mem_nonZeroDivisorsRight_of_constantCoeffproof · cited by 1
- MvPowerSeries.pderiv.extproof · cited by 1
- MvPowerSeries.constantCoeff_expandproof · cited by 0