Theorems · Theorem · commutative algebra
PowerSeries.subst_coe
∀ {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},
PowerSeries.HasSubst a → ∀ (p : Polynomial R), PowerSeries.subst a ↑p = (Polynomial.aeval a) p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 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
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- PowerSeriesproof · cited by 797
- MvPowerSeriesstatement and proof · cited by 659
- Polynomial.aevalstatement and proof · cited by 615
- Polynomial.toPowerSeriesstatement and proof · cited by 96
- PowerSeries.HasSubststatement and proof · cited by 67
- PowerSeries.subststatement · cited by 58
- PowerSeries.coe_substAlgHomproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.subst_rescale_of_degree_eq_oneproof · cited by 0