Theorems · Theorem · commutative algebra
PowerSeries.le_order_subst_left
∀ {R : Type u_2} [inst : CommRing R] {τ : Type u_3} {f : MvPowerSeries τ R} {φ : PowerSeries R},
MvPowerSeries.constantCoeff f = 0 → φ.order ≤ (PowerSeries.subst f φ).order- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 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.
Cites15
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
- ENatstatement · cited by 4,985
- LE.le.transproof · cited by 3,151
- PowerSeriesstatement and proof · cited by 797
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.constantCoeffstatement and proof · cited by 98
- PowerSeries.orderstatement and proof · cited by 92
- PowerSeries.subststatement · cited by 58
- MvPowerSeries.orderstatement · cited by 45
- PowerSeries.HasSubst.of_constantCoeff_zeroproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.le_order_subst_left'proof · cited by 0