Loogle!

Result

Found 10 declarations mentioning RCLike.map.

• RCLike.map 📋 Mathlib.Analysis.RCLike.Basic
  (𝕜 : Type u_3) (𝕜' : Type u_4) [RCLike 𝕜] [RCLike 𝕜'] : 𝕜 →L[ℝ] 𝕜'
• RCLike.map_from_real 📋 Mathlib.Analysis.RCLike.Basic
  {K : Type u_1} [RCLike K] : RCLike.map ℝ K = RCLike.ofRealCLM
• RCLike.map_to_real 📋 Mathlib.Analysis.RCLike.Basic
  {K : Type u_1} [RCLike K] : RCLike.map K ℝ = RCLike.reCLM
• RCLike.map_same_eq_id 📋 Mathlib.Analysis.RCLike.Basic
  {K : Type u_1} [RCLike K] : RCLike.map K K = ContinuousLinearMap.id ℝ K
• RCLike.map_apply 📋 Mathlib.Analysis.RCLike.Basic
  (𝕜 : Type u_3) (𝕜' : Type u_4) [RCLike 𝕜] [RCLike 𝕜'] (x : 𝕜) : (RCLike.map 𝕜 𝕜') x = ↑(RCLike.re x) + ↑(RCLike.im x) * RCLike.I
• RCLike.toContinuousLinearMap_complexLinearIsometryEquiv 📋 Mathlib.Analysis.Complex.Basic
  {𝕜 : Type u_2} [RCLike 𝕜] (h : RCLike.im RCLike.I = 1) : ↑(RCLike.complexLinearIsometryEquiv h).toContinuousLinearEquiv = RCLike.map 𝕜 ℂ
• RCLike.map_nonneg_iff 📋 Mathlib.Analysis.Complex.Basic
  {𝕜 : Type u_2} {𝕜' : Type u_3} [RCLike 𝕜] [RCLike 𝕜'] (h : RCLike.im RCLike.I = 1) {a : 𝕜} : 0 ≤ (RCLike.map 𝕜 𝕜') a ↔ 0 ≤ a
• RCLike.sqrt.eq_1 📋 Mathlib.Analysis.RCLike.Sqrt
  {𝕜 : Type u_1} [RCLike 𝕜] (a : 𝕜) : RCLike.sqrt a = (RCLike.map ℂ 𝕜) ((RCLike.map 𝕜 ℂ) a).sqrt
• Complex.sqrt_map 📋 Mathlib.Analysis.RCLike.Sqrt
  {𝕜 : Type u_1} [RCLike 𝕜] {a : 𝕜} (h : RCLike.im RCLike.I = 1) : ((RCLike.map 𝕜 ℂ) a).sqrt = (RCLike.map 𝕜 ℂ) (RCLike.sqrt a)
• RCLike.sqrt_map 📋 Mathlib.Analysis.RCLike.Sqrt
  {𝕜 : Type u_1} [RCLike 𝕜] {𝕜' : Type u_2} [RCLike 𝕜'] {a : 𝕜} (h : RCLike.im RCLike.I = RCLike.im RCLike.I) : RCLike.sqrt ((RCLike.map 𝕜 𝕜') a) = (RCLike.map 𝕜 𝕜') (RCLike.sqrt a)

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 36960b0 serving mathlib revision 9a4cf1d