Theorems · Theorem · commutative algebra
PowerSeries.substAlgHom_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} (ha : PowerSeries.HasSubst a) (p : Polynomial R),
(PowerSeries.substAlgHom ha) ↑p = (Polynomial.aeval a) p- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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 and proof · cited by 3,236
- PowerSeriesstatement and proof · cited by 797
- MvPowerSeriesstatement and proof · cited by 659
- Polynomial.aevalstatement and proof · cited by 615
- MvPolynomial.Xproof · cited by 552
- MvPolynomial.aevalproof · cited by 298
- Polynomial.aeval_Xproof · cited by 120
- MvPolynomial.aeval_Xproof · cited by 105
Cited by2
Results whose statement or proof uses this declaration.
- PowerSeries.substAlgHom_Xproof · cited by 2
- PowerSeries.subst_coeproof · cited by 1