Theorems · Theorem · commutative algebra
MvPowerSeries.HasSubst.mul_left
∀ {σ : Type u_1} {τ : Type u_4} {S : Type u_5} [inst : CommRing S] (b : σ → MvPowerSeries τ S)
{a : σ → MvPowerSeries τ S}, MvPowerSeries.HasSubst a → MvPowerSeries.HasSubst (b * a)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 103 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.
Cites7
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
- Bot.botproof · cited by 4,720
- UniformSpaceproof · cited by 2,040
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.HasSubststatement and proof · cited by 74
- MvPowerSeries.hasSubst_iff_hasEval_of_discreteTopologyproof · cited by 5
- MvPowerSeries.HasEval.mul_leftproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- MvPowerSeries.HasSubst.smul_Xproof · cited by 4
- MvPowerSeries.hasSubstIdealproof · cited by 1
- MvPowerSeries.HasSubst.smulproof · cited by 0
- MvPowerSeries.HasSubst.mul_rightproof · cited by 0