Theorems · Theorem · commutative algebra
PowerSeries.HasSubst.of_constantCoeff_zero
∀ {τ : Type u_3} {S : Type u_4} [inst : CommRing S] {a : MvPowerSeries τ S},
MvPowerSeries.constantCoeff a = 0 → PowerSeries.HasSubst a- Cited by
- 6 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- MvPowerSeriesstatement and proof · cited by 659
- IsNilpotentproof · cited by 248
- MvPowerSeries.constantCoeffstatement and proof · cited by 98
- PowerSeries.HasSubststatement · cited by 67
Cited by6
Results whose statement or proof uses this declaration.
- PowerSeries.HasSubst.of_constantCoeff_zero'proof · cited by 7
- PowerSeries.HasSubst.monomialproof · cited by 1
- PowerSeries.le_order_subst_leftproof · cited by 1
- PowerSeries.le_order_subst_rightproof · cited by 1
- PowerSeries.constantCoeff_subst_eq_zeroproof · cited by 1
- PowerSeries.subst_rescale_of_degree_eq_oneproof · cited by 0