Theorems · Theorem · commutative algebra
PowerSeries.constantCoeff_subst_eq_zero
∀ {R : Type u_2} [inst : CommRing R] {τ : Type u_3} {S : Type u_4} [inst_1 : CommRing S] [inst_2 : Algebra R S]
{a : MvPowerSeries τ S},
MvPowerSeries.constantCoeff a = 0 →
∀ (f : PowerSeries R), PowerSeries.constantCoeff f = 0 → MvPowerSeries.constantCoeff (PowerSeries.subst a f) = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- PowerSeriesstatement and proof · cited by 797
- MvPowerSeriesstatement and proof · cited by 659
- PowerSeries.constantCoeffstatement and proof · cited by 126
- MvPowerSeries.constantCoeffstatement and proof · cited by 98
- MvPowerSeries.substproof · cited by 73
- PowerSeries.subststatement · cited by 58
- MvPowerSeries.constantCoeff_subst_eq_zeroproof · cited by 7
- PowerSeries.HasSubst.of_constantCoeff_zeroproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.constantCoeff_logOfproof · cited by 0