Loogle!

Result

Found 6 declarations mentioning MvPowerSeries.HasEval.map.

• MvPowerSeries.HasEval.map 📋 Mathlib.RingTheory.MvPowerSeries.Evaluation
  {σ : Type u_1} {R : Type u_2} [CommRing R] [TopologicalSpace R] {S : Type u_3} [CommRing S] [TopologicalSpace S] {φ : R →+* S} (hφ : Continuous ⇑φ) {a : σ → R} (ha : MvPowerSeries.HasEval a) : MvPowerSeries.HasEval fun s => φ (a s)
• MvPowerSeries.comp_aeval 📋 Mathlib.RingTheory.MvPowerSeries.Evaluation
  {σ : Type u_1} {R : Type u_2} [CommRing R] [UniformSpace R] {S : Type u_3} [CommRing S] [UniformSpace S] {a : σ → S} [IsTopologicalSemiring R] [IsUniformAddGroup R] [IsUniformAddGroup S] [CompleteSpace S] [T2Space S] [IsTopologicalRing S] [IsLinearTopology S S] [Algebra R S] [ContinuousSMul R S] (ha : MvPowerSeries.HasEval a) {T : Type u_4} [CommRing T] [UniformSpace T] [IsUniformAddGroup T] [IsTopologicalRing T] [IsLinearTopology T T] [T2Space T] [Algebra R T] [ContinuousSMul R T] [CompleteSpace T] {ε : S →ₐ[R] T} (hε : Continuous ⇑ε) : ε.comp (MvPowerSeries.aeval ha) = MvPowerSeries.aeval ⋯
• MvPowerSeries.aeval_unique 📋 Mathlib.RingTheory.MvPowerSeries.Evaluation
  {σ : Type u_1} {R : Type u_2} [CommRing R] [UniformSpace R] {S : Type u_3} [CommRing S] [UniformSpace S] [IsTopologicalSemiring R] [IsUniformAddGroup R] [IsUniformAddGroup S] [CompleteSpace S] [T2Space S] [IsTopologicalRing S] [IsLinearTopology S S] [Algebra R S] [ContinuousSMul R S] {ε : MvPowerSeries σ R →ₐ[R] S} (hε : Continuous ⇑ε) : MvPowerSeries.aeval ⋯ = ε
• MvPowerSeries.comp_substAlgHom 📋 Mathlib.RingTheory.MvPowerSeries.Substitution
  {σ : Type u_1} {R : Type u_3} [CommRing R] {τ : Type u_4} {S : Type u_5} [CommRing S] [Algebra R S] {a : σ → MvPowerSeries τ S} {T : Type u_6} [CommRing T] [UniformSpace T] [T2Space T] [CompleteSpace T] [IsUniformAddGroup T] [IsTopologicalRing T] [IsLinearTopology T T] [Algebra R T] {ε : MvPowerSeries τ S →ₐ[R] T} [UniformSpace R] [DiscreteUniformity R] [UniformSpace S] [DiscreteUniformity S] (ha : MvPowerSeries.HasSubst a) (hε : Continuous ⇑ε) : ε.comp (MvPowerSeries.substAlgHom ha) = MvPowerSeries.aeval ⋯
• MvPowerSeries.comp_subst_apply 📋 Mathlib.RingTheory.MvPowerSeries.Substitution
  {σ : Type u_1} {R : Type u_3} [CommRing R] {τ : Type u_4} {S : Type u_5} [CommRing S] [Algebra R S] {a : σ → MvPowerSeries τ S} {T : Type u_6} [CommRing T] [UniformSpace T] [T2Space T] [CompleteSpace T] [IsUniformAddGroup T] [IsTopologicalRing T] [IsLinearTopology T T] [Algebra R T] {ε : MvPowerSeries τ S →ₐ[R] T} [UniformSpace R] [DiscreteUniformity R] [UniformSpace S] [DiscreteUniformity S] (ha : MvPowerSeries.HasSubst a) (hε : Continuous ⇑ε) (f : MvPowerSeries σ R) : ε (MvPowerSeries.subst a f) = (MvPowerSeries.aeval ⋯) f
• MvPowerSeries.comp_subst 📋 Mathlib.RingTheory.MvPowerSeries.Substitution
  {σ : Type u_1} {R : Type u_3} [CommRing R] {τ : Type u_4} {S : Type u_5} [CommRing S] [Algebra R S] {a : σ → MvPowerSeries τ S} {T : Type u_6} [CommRing T] [UniformSpace T] [T2Space T] [CompleteSpace T] [IsUniformAddGroup T] [IsTopologicalRing T] [IsLinearTopology T T] [Algebra R T] {ε : MvPowerSeries τ S →ₐ[R] T} [UniformSpace R] [DiscreteUniformity R] [UniformSpace S] [DiscreteUniformity S] (ha : MvPowerSeries.HasSubst a) (hε : Continuous ⇑ε) : ⇑ε ∘ MvPowerSeries.subst a = ⇑(MvPowerSeries.aeval ⋯)

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.

This is Loogle revision 19971e9 serving mathlib revision bce1d65