Theorems · Theorem · commutative algebra
MvPowerSeries.HasEval.mul_left
∀ {σ : Type u_1} {S : Type u_3} [inst : CommRing S] [inst_1 : TopologicalSpace S] [IsLinearTopology S S] (c : σ → S)
{x : σ → S}, MvPowerSeries.HasEval x → MvPowerSeries.HasEval (c * x)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- CommRingstatement and proof · cited by 17,173
- IsLinearTopologystatement and proof · cited by 83
- MvPowerSeries.HasEvalstatement and proof · cited by 37
- MvPowerSeries.HasEval.hpowproof · cited by 6
- MvPowerSeries.HasEval.tendsto_zeroproof · cited by 6
- IsLinearTopology.tendsto_mul_zero_of_rightproof · cited by 2
- IsTopologicallyNilpotent.mul_leftproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- MvPowerSeries.hasEvalIdealproof · cited by 3
- MvPowerSeries.HasSubst.mul_leftproof · cited by 3
- PowerSeries.HasEval.mul_leftproof · cited by 1
- MvPowerSeries.mem_hasEvalIdeal_iffproof · cited by 1
- MvPowerSeries.HasEval.mul_rightproof · cited by 1