Loogle!

Result

Found 38 declarations mentioning Matroid.map.

• Matroid.map 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} (M : Matroid α) (f : α → β) (hf : Set.InjOn f M.E) : Matroid β
• Matroid.map_id 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {M : Matroid α} : M.map id ⋯ = M
• Matroid.instFinitaryMap 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {M : Matroid α} [M.Finitary] {f : α → β} (hf : Set.InjOn f M.E) : (M.map f hf).Finitary
• Matroid.instFiniteMap 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {M : Matroid α} [M.Finite] {f : α → β} (hf : Set.InjOn f M.E) : (M.map f hf).Finite
• Matroid.instNonemptyMap 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {M : Matroid α} [M.Nonempty] {f : α → β} (hf : Set.InjOn f M.E) : (M.map f hf).Nonempty
• Matroid.instRankFiniteMap 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {M : Matroid α} [M.RankFinite] {f : α → β} (hf : Set.InjOn f M.E) : (M.map f hf).RankFinite
• Matroid.instRankPosMap 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {M : Matroid α} [M.RankPos] {f : α → β} (hf : Set.InjOn f M.E) : (M.map f hf).RankPos
• Matroid.map_emptyOn 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} (f : α → β) : (Matroid.emptyOn α).map f ⋯ = Matroid.emptyOn β
• Matroid.comap_map 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {M : Matroid α} {f : α → β} (hf : Function.Injective f) : (M.map f ⋯).comap f = M
• Matroid.map_ground 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} (M : Matroid α) (f : α → β) (hf : Set.InjOn f M.E) : (M.map f hf).E = f '' M.E
• Matroid.map_dual 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {f : α → β} {M : Matroid α} {hf : Set.InjOn f M.E} : (M.map f hf)✶ = M✶.map f hf
• Matroid.Indep.map 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {I : Set α} {M : Matroid α} (hI : M.Indep I) (f : α → β) (hf : Set.InjOn f M.E) : (M.map f hf).Indep (f '' I)
• Matroid.IsBase.map 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {M : Matroid α} {B : Set α} (hB : M.IsBase B) {f : α → β} (hf : Set.InjOn f M.E) : (M.map f hf).IsBase (f '' B)
• Matroid.map_freeOn 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {E : Set α} (f : α → β) (hf : Set.InjOn f (Matroid.freeOn E).E) : (Matroid.freeOn E).map f hf = Matroid.freeOn (f '' E)
• Matroid.map_loopyOn 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {E : Set α} (f : α → β) (hf : Set.InjOn f (Matroid.loopyOn E).E) : (Matroid.loopyOn E).map f hf = Matroid.loopyOn (f '' E)
• Matroid.mapEmbedding.eq_1 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} (M : Matroid α) (f : α ↪ β) : M.mapEmbedding f = M.map ⇑f ⋯
• Matroid.Indep.exists_bijOn_of_map 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {f : α → β} {M : Matroid α} {I : Set β} (hf : Set.InjOn f M.E) (hI : (M.map f hf).Indep I) : ∃ I₀, M.Indep I₀ ∧ Set.BijOn f I₀ I
• Matroid.IsBasis.map 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {I : Set α} {M : Matroid α} {X : Set α} (hIX : M.IsBasis I X) {f : α → β} (hf : Set.InjOn f M.E) : (M.map f hf).IsBasis (f '' I) (f '' X)
• Matroid.map_image_indep_iff 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {f : α → β} {M : Matroid α} {hf : Set.InjOn f M.E} {I : Set α} (hI : I ⊆ M.E) : (M.map f hf).Indep (f '' I) ↔ M.Indep I
• Matroid.map_image_isBase_iff 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {f : α → β} {M : Matroid α} {hf : Set.InjOn f M.E} {B : Set α} (hB : B ⊆ M.E) : (M.map f hf).IsBase (f '' B) ↔ M.IsBase B
• Matroid.map_comap 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {N : Matroid β} {f : α → β} (h_range : N.E ⊆ Set.range f) (hf : Set.InjOn f (f ⁻¹' N.E)) : (N.comap f).map f hf = N
• Matroid.map_dep_iff 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {f : α → β} {M : Matroid α} {hf : Set.InjOn f M.E} {D : Set β} : (M.map f hf).Dep D ↔ ∃ D₀, M.Dep D₀ ∧ D = f '' D₀
• Matroid.map_indep_iff 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {f : α → β} {M : Matroid α} {hf : Set.InjOn f M.E} {I : Set β} : (M.map f hf).Indep I ↔ ∃ I₀, M.Indep I₀ ∧ I = f '' I₀
• Matroid.map_isBase_iff 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} (M : Matroid α) (f : α → β) (hf : Set.InjOn f M.E) {B : Set β} : (M.map f hf).IsBase B ↔ ∃ B₀, M.IsBase B₀ ∧ B = f '' B₀
• Matroid.mapEquiv_eq_map 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {M : Matroid α} (f : α ≃ β) : M.mapEquiv f = M.map ⇑f ⋯
• Matroid.map_isBasis_iff 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {M : Matroid α} {I X : Set α} (f : α → β) (hf : Set.InjOn f M.E) (hI : I ⊆ M.E) (hX : X ⊆ M.E) : (M.map f hf).IsBasis (f '' I) (f '' X) ↔ M.IsBasis I X
• Matroid.map_isBasis_iff' 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} {β : Type u_2} {f : α → β} {M : Matroid α} {I X : Set β} {hf : Set.InjOn f M.E} : (M.map f hf).IsBasis I X ↔ ∃ I₀ X₀, M.IsBasis I₀ X₀ ∧ I = f '' I₀ ∧ X = f '' X₀
• Matroid.map_val_restrictSubtype_eq 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} (M : Matroid α) (X : Set α) : (M.restrictSubtype X).map Subtype.val ⋯ = M.restrict X
• Matroid.map_val_restrictSubtype_ground_eq 📋 Mathlib.Data.Matroid.Map
  {α : Type u_1} (M : Matroid α) : (M.restrictSubtype M.E).map Subtype.val ⋯ = M
• Matroid.map_closure_eq 📋 Mathlib.Data.Matroid.Closure
  {α : Type u_2} {β : Type u_3} (M : Matroid α) (f : α → β) (hf : Set.InjOn f M.E) (X : Set β) : (M.map f hf).closure X = f '' M.closure (f ⁻¹' X)
• Matroid.map_loops 📋 Mathlib.Data.Matroid.Loop
  {α : Type u_1} {β : Type u_2} {M : Matroid α} {f : α → β} {hf : Set.InjOn f M.E} : (M.map f hf).loops = f '' M.loops
• Matroid.map_isLoop_iff 📋 Mathlib.Data.Matroid.Loop
  {α : Type u_1} {β : Type u_2} {M : Matroid α} {e : α} {f : α → β} {hf : Set.InjOn f M.E} (he : e ∈ M.E := by aesop_mat) : (M.map f hf).IsLoop (f e) ↔ M.IsLoop e
• Matroid.eRank_map 📋 Mathlib.Data.Matroid.Rank.ENat
  {α : Type u_1} {β : Type u_2} {f : α → β} (M : Matroid α) (hf : Set.InjOn f M.E) : (M.map f hf).eRank = M.eRank
• Matroid.eRk_map 📋 Mathlib.Data.Matroid.Rank.ENat
  {α : Type u_1} {X : Set α} {β : Type u_2} {f : α → β} (M : Matroid α) (hf : Set.InjOn f M.E) (hX : X ⊆ M.E := by aesop_mat) : (M.map f hf).eRk (f '' X) = M.eRk X
• Matroid.invariantCardinalRank_map 📋 Mathlib.Data.Matroid.Rank.Cardinal
  {α : Type u} {β : Type v} {f : α → β} (M : Matroid α) [M.InvariantCardinalRank] (hf : Set.InjOn f M.E) : (M.map f hf).InvariantCardinalRank
• Matroid.cRk_map_eq 📋 Mathlib.Data.Matroid.Rank.Cardinal
  {α β : Type u} {f : α → β} {X : Set β} (M : Matroid α) (hf : Set.InjOn f M.E) : (M.map f hf).cRk X = M.cRk (f ⁻¹' X)
• Matroid.cRk_map_image 📋 Mathlib.Data.Matroid.Rank.Cardinal
  {α β : Type u} {f : α → β} (M : Matroid α) (hf : Set.InjOn f M.E) (X : Set α) (hX : X ⊆ M.E := by aesop_mat) : (M.map f hf).cRk (f '' X) = M.cRk X
• Matroid.cRk_map_image_lift 📋 Mathlib.Data.Matroid.Rank.Cardinal
  {α : Type u} {β : Type v} {f : α → β} (M : Matroid α) (hf : Set.InjOn f M.E) (X : Set α) (hX : X ⊆ M.E := by aesop_mat) : Cardinal.lift.{u, v} ((M.map f hf).cRk (f '' X)) = Cardinal.lift.{v, u} (M.cRk X)

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