Loogle!

Result

Found 9 declarations mentioning SimpleGraph.ConnectedComponent.map.

• SimpleGraph.ConnectedComponent.map 📋 Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
  {V : Type u} {V' : Type v} {G : SimpleGraph V} {G' : SimpleGraph V'} (φ : G →g G') (C : G.ConnectedComponent) : G'.ConnectedComponent
• SimpleGraph.ConnectedComponent.map_id 📋 Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
  {V : Type u} {G : SimpleGraph V} (C : G.ConnectedComponent) : SimpleGraph.ConnectedComponent.map SimpleGraph.Hom.id C = C
• SimpleGraph.ConnectedComponent.surjective_map_ofLE 📋 Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
  {V : Type u} {G G' : SimpleGraph V} (h : G ≤ G') : Function.Surjective (SimpleGraph.ConnectedComponent.map (SimpleGraph.Hom.ofLE h))
• SimpleGraph.ConnectedComponent.map_mk 📋 Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
  {V : Type u} {V' : Type v} {G : SimpleGraph V} {G' : SimpleGraph V'} (φ : G →g G') (v : V) : SimpleGraph.ConnectedComponent.map φ (G.connectedComponentMk v) = G'.connectedComponentMk (φ v)
• SimpleGraph.ConnectedComponent.map_comp 📋 Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
  {V : Type u} {V' : Type v} {V'' : Type w} {G : SimpleGraph V} {G' : SimpleGraph V'} {G'' : SimpleGraph V''} (C : G.ConnectedComponent) (φ : G →g G') (ψ : G' →g G'') : SimpleGraph.ConnectedComponent.map ψ (SimpleGraph.ConnectedComponent.map φ C) = SimpleGraph.ConnectedComponent.map (ψ.comp φ) C
• SimpleGraph.ConnectedComponent.iso_image_comp_eq_map_iff_eq_comp 📋 Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
  {V : Type u} {V' : Type v} {G : SimpleGraph V} {G' : SimpleGraph V'} {φ : G ≃g G'} {v : V} {C : G.ConnectedComponent} : G'.connectedComponentMk (φ v) = SimpleGraph.ConnectedComponent.map (RelIso.toRelEmbedding φ).toRelHom C ↔ G.connectedComponentMk v = C
• SimpleGraph.ConnectedComponent.iso_inv_image_comp_eq_iff_eq_map 📋 Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
  {V : Type u} {V' : Type v} {G : SimpleGraph V} {G' : SimpleGraph V'} {φ : G ≃g G'} {v' : V'} {C : G.ConnectedComponent} : G.connectedComponentMk (φ.symm v') = C ↔ G'.connectedComponentMk v' = SimpleGraph.ConnectedComponent.map (RelIso.toRelEmbedding φ).toRelHom C
• SimpleGraph.Iso.connectedComponentEquiv_apply 📋 Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
  {V : Type u} {V' : Type v} {G : SimpleGraph V} {G' : SimpleGraph V'} (φ : G ≃g G') (C : G.ConnectedComponent) : φ.connectedComponentEquiv C = SimpleGraph.ConnectedComponent.map (RelIso.toRelEmbedding φ).toRelHom C
• SimpleGraph.Iso.connectedComponentEquiv_symm_apply 📋 Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
  {V : Type u} {V' : Type v} {G : SimpleGraph V} {G' : SimpleGraph V'} (φ : G ≃g G') (C : G'.ConnectedComponent) : φ.connectedComponentEquiv.symm C = SimpleGraph.ConnectedComponent.map (RelIso.toRelEmbedding φ.symm).toRelHom C

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 6ff4759 serving mathlib revision edaf32c