Loogle!

Result

Found 12 declarations mentioning Affine.Simplex.map.

• Affine.Simplex.map_id 📋 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.map (AffineMap.id k P) ⋯ = s
• Affine.Simplex.map 📋 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) : Affine.Simplex k P₂ n
• Affine.Simplex.map_mkOfPoint 📋 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] (f : P →ᵃ[k] P₂) (hf : Function.Injective ⇑f) (p : P) : (Affine.Simplex.mkOfPoint k p).map f hf = Affine.Simplex.mkOfPoint k (f p)
• Affine.Simplex.reindex_map 📋 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] {m n : ℕ} (s : Affine.Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) (f : P →ᵃ[k] P₂) (hf : Function.Injective ⇑f) : (s.map f hf).reindex e = (s.reindex e).map f hf
• Affine.Simplex.map_points 📋 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) : (s.map f hf).points = ⇑f ∘ s.points
• Affine.Simplex.faceOpposite_map 📋 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} [NeZero n] (s : Affine.Simplex k P n) (f : P →ᵃ[k] P₂) (hf : Function.Injective ⇑f) (i : Fin (n + 1)) : (s.map f hf).faceOpposite i = (s.faceOpposite i).map f hf
• Affine.Simplex.face_map 📋 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) {fs : Finset (Fin (n + 1))} {m : ℕ} (h : fs.card = m + 1) : (s.map f hf).face h = (s.face h).map f hf
• Affine.Simplex.map_comp 📋 Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
  {k : Type u_1} {V : Type u_2} {V₂ : Type u_3} {V₃ : Type u_4} {P : Type u_5} {P₂ : Type u_6} {P₃ : Type u_7} [Ring k] [AddCommGroup V] [AddCommGroup V₂] [AddCommGroup V₃] [Module k V] [Module k V₂] [Module k V₃] [AddTorsor V P] [AddTorsor V₂ P₂] [AddTorsor V₃ P₃] {n : ℕ} (s : Affine.Simplex k P n) (f : P →ᵃ[k] P₂) (hf : Function.Injective ⇑f) (g : P₂ →ᵃ[k] P₃) (hg : Function.Injective ⇑g) : s.map (g.comp f) ⋯ = (s.map f hf).map g hg
• 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