Theorems · Theorem · commutative algebra
MvPowerSeries.HasSubst.hasEval
∀ {σ : Type u_1} {τ : Type u_4} {S : Type u_5} [inst : CommRing S] {a : σ → MvPowerSeries τ S}
[inst_1 : TopologicalSpace S], MvPowerSeries.HasSubst a → MvPowerSeries.HasEval a- Cited by
- 14 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingTopologicalSpace
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
- MvPowerSeriesstatement and proof · cited by 659
- bot_leproof · cited by 306
- MvPowerSeries.HasSubststatement and proof · cited by 74
- MvPowerSeries.HasEvalstatement · cited by 37
- MvPowerSeries.hasSubst_iff_hasEval_of_discreteTopologyproof · cited by 5
- MvPowerSeries.HasEval.monoproof · cited by 2
Cited by14
Results whose statement or proof uses this declaration.
- MvPowerSeries.coe_substAlgHomproof · cited by 15
- MvPowerSeries.coeff_substproof · cited by 15
- MvPowerSeries.substAlgHom_eq_aevalstatement and proof · cited by 6
- MvPowerSeries.coeff_subst_finiteproof · cited by 6
- MvPowerSeries.HasSubst.compproof · cited by 4
- MvPowerSeries.substAlgHom_comp_substAlgHomproof · cited by 3
- PowerSeries.substAlgHom_eq_aevalproof · cited by 2
- MvPowerSeries.continuous_substproof · cited by 2
- MvPowerSeries.comp_subststatement · cited by 1
- MvPowerSeries.comp_substAlgHomstatement and proof · cited by 1
- MvPowerSeries.comp_subst_applystatement · cited by 1
- MvPowerSeries.eval₂_substproof · cited by 0