Theorems · Theorem · commutative algebra
MvPowerSeries.hasSubst_of_constantCoeff_zero
∀ {σ : Type u_1} {τ : Type u_4} {S : Type u_5} [inst : CommRing S] [Finite σ] {a : σ → MvPowerSeries τ S},
(∀ (s : σ), MvPowerSeries.constantCoeff (a s) = 0) → MvPowerSeries.HasSubst aIf σ is finite, then having zero constant coefficient is enough for HasSubst
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Finitestatement and proof · cited by 3,029
- MvPowerSeriesstatement and proof · cited by 659
- IsNilpotentproof · cited by 248
- MvPowerSeries.constantCoeffstatement and proof · cited by 98
- MvPowerSeries.HasSubststatement · cited by 74
- MvPowerSeries.hasSubst_of_constantCoeff_nilpotentproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- MvPowerSeries.HasSubst.X_zeroproof · cited by 4
- MvPowerSeries.HasSubst.zero_Xproof · cited by 4
- MvPowerSeries.HasSubst.X_Xproof · cited by 4
- MvPowerSeries.HasSubst.cons_subst_zero_leftproof · cited by 1
- MvPowerSeries.HasSubst.cons_subst_zero_rightproof · cited by 1
- MvPowerSeries.truncTotal_subst_of_leproof · cited by 1
- MvPowerSeries.truncTotal_subst_eq_truncTotal_truncTotal_substproof · cited by 0
- PowerSeries.coeff_subst_X_zero_add_X_oneproof · cited by 0