Loogle!

Result

Found 11 declarations mentioning Nonempty.map.

• Nonempty.map 📋 Mathlib.Logic.Nonempty
  {α : Sort u_3} {β : Sort u_4} (f : α → β) : Nonempty α → Nonempty β
• AffineSubspace.inclusion 📋 Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic
  {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_3} [Ring k] [AddCommGroup V₁] [Module k V₁] [AddTorsor V₁ P₁] {S₁ S₂ : AffineSubspace k P₁} [Nonempty ↥S₁] (h : S₁ ≤ S₂) : ↥S₁ →ᵃ[k] ↥S₂
• AffineSubspace.inclusion_rfl 📋 Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic
  {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_3} [Ring k] [AddCommGroup V₁] [Module k V₁] [AddTorsor V₁ P₁] {S₁ : AffineSubspace k P₁} [Nonempty ↥S₁] : AffineSubspace.inclusion ⋯ = AffineMap.id k ↥S₁
• AffineSubspace.inclusion_linear 📋 Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic
  {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_3} [Ring k] [AddCommGroup V₁] [Module k V₁] [AddTorsor V₁ P₁] {S₁ S₂ : AffineSubspace k P₁} [Nonempty ↥S₁] (h : S₁ ≤ S₂) : (AffineSubspace.inclusion h).linear = Submodule.inclusion ⋯
• AffineSubspace.coe_inclusion_apply 📋 Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic
  {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_3} [Ring k] [AddCommGroup V₁] [Module k V₁] [AddTorsor V₁ P₁] {S₁ S₂ : AffineSubspace k P₁} [Nonempty ↥S₁] (h : S₁ ≤ S₂) (x : ↥S₁) : ↑((AffineSubspace.inclusion h) x) = ↑x
• Affine.Simplex.restrict 📋 Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
  {k : Type u_1} {V : Type u_2} {P : Type u_5} [Ring k] [AddCommGroup V] [Module k V] [AddTorsor V P] {n : ℕ} (s : Affine.Simplex k P n) (S : AffineSubspace k P) (hS : affineSpan k (Set.range s.points) ≤ S) : Affine.Simplex k (↥S) n
• Affine.Simplex.restrict_points_coe 📋 Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
  {k : Type u_1} {V : Type u_2} {P : Type u_5} [Ring k] [AddCommGroup V] [Module k V] [AddTorsor V P] {n : ℕ} (s : Affine.Simplex k P n) (S : AffineSubspace k P) (hS : affineSpan k (Set.range s.points) ≤ S) (i : Fin (n + 1)) : ↑((s.restrict S hS).points i) = s.points i
• Affine.Simplex.restrict_map_subtype 📋 Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
  {k : Type u_1} {V : Type u_2} {P : Type u_5} [Ring k] [AddCommGroup V] [Module k V] [AddTorsor V P] {n : ℕ} (s : Affine.Simplex k P n) : (s.restrict (affineSpan k (Set.range s.points)) ⋯).map (affineSpan k (Set.range s.points)).subtype ⋯ = s
• Affine.Simplex.restrict_map_inclusion 📋 Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
  {k : Type u_1} {V : Type u_2} {P : Type u_5} [Ring k] [AddCommGroup V] [Module k V] [AddTorsor V P] {n : ℕ} (s : Affine.Simplex k P n) (S₁ S₂ : AffineSubspace k P) (hS₁ : affineSpan k (Set.range s.points) ≤ S₁) (hS₂ : S₁ ≤ S₂) : (s.restrict S₁ hS₁).map (AffineSubspace.inclusion hS₂) ⋯ = s.restrict S₂ ⋯
• Affine.Simplex.map_subtype_restrict 📋 Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
  {k : Type u_1} {V : Type u_2} {P : Type u_5} [Ring k] [AddCommGroup V] [Module k V] [AddTorsor V P] {n : ℕ} (S : AffineSubspace k P) [Nonempty ↥S] (s : Affine.Simplex k (↥S) n) : (s.map S.subtype ⋯).restrict S ⋯ = s
• Affine.Simplex.restrict_map_restrict 📋 Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
  {k : Type u_1} {V : Type u_2} {V₂ : Type u_3} {P : Type u_5} {P₂ : Type u_6} [Ring k] [AddCommGroup V] [AddCommGroup V₂] [Module k V] [Module k V₂] [AddTorsor V P] [AddTorsor V₂ P₂] {n : ℕ} (s : Affine.Simplex k P n) (f : P →ᵃ[k] P₂) (hf : Function.Injective ⇑f) (S₁ : AffineSubspace k P) (S₂ : AffineSubspace k P₂) (hS₁ : affineSpan k (Set.range s.points) ≤ S₁) (hfS : AffineSubspace.map f S₁ ≤ S₂) : (s.restrict S₁ hS₁).map (f.restrict hfS) ⋯ = (s.map f hf).restrict S₂ ⋯

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 ff04530 serving mathlib revision 8623f65