Theorems · Theorem · commutative algebra
PowerSeries.hasSubst_iff
∀ {τ : Type u_3} {S : Type u_4} [inst : CommRing S] {a : MvPowerSeries τ S},
PowerSeries.HasSubst a ↔ MvPowerSeries.HasSubst (Function.const Unit a)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 96 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.
Cites6
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
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.HasSubststatement and proof · cited by 74
- PowerSeries.HasSubststatement and proof · cited by 67
- MvPowerSeries.HasSubst.const_coeffproof · cited by 5
- MvPowerSeries.hasSubst_of_constantCoeff_nilpotentproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- PowerSeries.HasSubst.constproof · cited by 15
- PowerSeries.le_order_substproof · cited by 2
- PowerSeries.HasSubst.zeroproof · cited by 1
- PowerSeries.constantCoeff_subst_eq_zeroproof · cited by 1
- PowerSeries.le_weightedOrder_substproof · cited by 0
- PowerSeries.hasSubst_iff_hasEval_of_discreteTopologyproof · cited by 0