Loogle!

Result

Found 21 declarations mentioning SimpleGraph.Subgraph.map.

• SimpleGraph.Subgraph.map 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} (f : G →g G') (H : G.Subgraph) : G'.Subgraph
• SimpleGraph.Subgraph.map_id 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {G : SimpleGraph V} (H : G.Subgraph) : SimpleGraph.Subgraph.map SimpleGraph.Hom.id H = H
• SimpleGraph.Subgraph.map_iso_top 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {H : SimpleGraph W} (e : G ≃g H) : SimpleGraph.Subgraph.map e.toHom ⊤ = ⊤
• SimpleGraph.map_singletonSubgraph 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} (f : G →g G') {v : V} : SimpleGraph.Subgraph.map f (G.singletonSubgraph v) = G'.singletonSubgraph (f v)
• SimpleGraph.Subgraph.map_hom_top 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {G : SimpleGraph V} (G' : G.Subgraph) : SimpleGraph.Subgraph.map G'.hom ⊤ = G'
• SimpleGraph.Subgraph.map_verts 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} (f : G →g G') (H : G.Subgraph) : (SimpleGraph.Subgraph.map f H).verts = ⇑f '' H.verts
• SimpleGraph.Subgraph.map_comp 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} {U : Type u_2} {G'' : SimpleGraph U} (H : G.Subgraph) (f : G →g G') (g : G' →g G'') : SimpleGraph.Subgraph.map (g.comp f) H = SimpleGraph.Subgraph.map g (SimpleGraph.Subgraph.map f H)
• SimpleGraph.Subgraph.map_sup 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} (f : G →g G') (H₁ H₂ : G.Subgraph) : SimpleGraph.Subgraph.map f (H₁ ⊔ H₂) = SimpleGraph.Subgraph.map f H₁ ⊔ SimpleGraph.Subgraph.map f H₂
• SimpleGraph.Subgraph.edgeSet_map 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} (f : G →g G') (H : G.Subgraph) : (SimpleGraph.Subgraph.map f H).edgeSet = Sym2.map ⇑f '' H.edgeSet
• SimpleGraph.Subgraph.map_monotone 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} {f : G →g G'} : Monotone (SimpleGraph.Subgraph.map f)
• SimpleGraph.Subgraph.map_adj 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} (f : G →g G') (H : G.Subgraph) (a✝ a✝¹ : W) : (SimpleGraph.Subgraph.map f H).Adj a✝ a✝¹ = Relation.Map H.Adj (⇑f) (⇑f) a✝ a✝¹
• SimpleGraph.map_subgraphOfAdj 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} (f : G →g G') {v w : V} (hvw : G.Adj v w) : SimpleGraph.Subgraph.map f (G.subgraphOfAdj hvw) = G'.subgraphOfAdj ⋯
• SimpleGraph.Subgraph.map_mono 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} {f : G →g G'} {H₁ H₂ : G.Subgraph} (hH : H₁ ≤ H₂) : SimpleGraph.Subgraph.map f H₁ ≤ SimpleGraph.Subgraph.map f H₂
• SimpleGraph.Subgraph.map_le_iff_le_comap 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} (f : G →g G') (H : G.Subgraph) (H' : G'.Subgraph) : SimpleGraph.Subgraph.map f H ≤ H' ↔ H ≤ SimpleGraph.Subgraph.comap f H'
• SimpleGraph.Subgraph.map.eq_1 📋 Mathlib.Combinatorics.SimpleGraph.Subgraph
  {V : Type u} {W : Type v} {G : SimpleGraph V} {G' : SimpleGraph W} (f : G →g G') (H : G.Subgraph) : SimpleGraph.Subgraph.map f H = { verts := ⇑f '' H.verts, Adj := Relation.Map H.Adj ⇑f ⇑f, adj_sub := ⋯, edge_vert := ⋯, symm := ⋯ }
• SimpleGraph.Walk.toSubgraph_map 📋 Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph
  {V : Type u} {V' : Type v} {G : SimpleGraph V} {G' : SimpleGraph V'} {u v : V} (f : G →g G') (p : G.Walk u v) : (SimpleGraph.Walk.map f p).toSubgraph = SimpleGraph.Subgraph.map f p.toSubgraph
• SimpleGraph.Copy.isoSubgraphMap 📋 Mathlib.Combinatorics.SimpleGraph.Copy
  {α : Type u_4} {β : Type u_5} {A : SimpleGraph α} {B : SimpleGraph β} (f : A.Copy B) (A' : A.Subgraph) : A'.coe ≃g (SimpleGraph.Subgraph.map f.toHom A').coe
• SimpleGraph.Subgraph.Copy.map 📋 Mathlib.Combinatorics.SimpleGraph.Copy
  {α : Type u_4} {β : Type u_5} {A : SimpleGraph α} {B : SimpleGraph β} (f : A.Copy B) (A' : A.Subgraph) : A'.coe ≃g (SimpleGraph.Subgraph.map f.toHom A').coe
• SimpleGraph.Subgraph.IsMatching.map_ofLE 📋 Mathlib.Combinatorics.SimpleGraph.Matching
  {V : Type u_1} {G G' : SimpleGraph V} {M : G.Subgraph} (h : M.IsMatching) (hGG' : G ≤ G') : (SimpleGraph.Subgraph.map (SimpleGraph.Hom.ofLE hGG') M).IsMatching
• SimpleGraph.Subgraph.Iso.isMatching_map 📋 Mathlib.Combinatorics.SimpleGraph.Matching
  {V : Type u_1} {W : Type u_2} {G : SimpleGraph V} {G' : SimpleGraph W} {M : G.Subgraph} (f : G ≃g G') : (SimpleGraph.Subgraph.map f.toHom M).IsMatching ↔ M.IsMatching
• SimpleGraph.Subgraph.IsMatching.map 📋 Mathlib.Combinatorics.SimpleGraph.Matching
  {V : Type u_1} {W : Type u_2} {G : SimpleGraph V} {G' : SimpleGraph W} {M : G.Subgraph} (f : G →g G') (hf : Function.Injective ⇑f) (hM : M.IsMatching) : (SimpleGraph.Subgraph.map f M).IsMatching

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