Theorems · Theorem · commutative algebra
PowerSeries.subst_X
∀ {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 → PowerSeries.subst a PowerSeries.X = a- Cited by
- 7 results in Mathlib
- Foundations
- Depth 117 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- PowerSeriesproof · cited by 797
- MvPowerSeriesstatement and proof · cited by 659
- PowerSeries.Xstatement and proof · cited by 183
- PowerSeries.HasSubststatement and proof · cited by 67
- PowerSeries.subststatement · cited by 58
- PowerSeries.coe_substAlgHomproof · cited by 12
- PowerSeries.substAlgHom_Xproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- PowerSeries.subst_substInv_leftproof · cited by 3
- FormalGroup.Xzero_eq_Xproof · cited by 1
- FormalGroup.Xzero_subst_Xzeroproof · cited by 1
- FormalGroup.zeroX_eq_Xproof · cited by 1
- FormalGroup.zeroX_subst_zeroXproof · cited by 1
- FormalGroup.zero_addproof · cited by 0
- FormalGroup.add_zeroproof · cited by 0