Theorems · Definition · combinatorics
SimpleGraph.induceHomOfLE
{V : Type u_1} → (G : SimpleGraph V) → {s s' : Set V} → s ⊆ s' → SimpleGraph.induce s G ↪g SimpleGraph.induce s' GGiven an inclusion of vertex subsets, the induced embedding on induced graphs.
This is not an abbreviation for induceHom since we get an embedding in this case.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Maps
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Function.Embeddingproof · cited by 988
- SimpleGraph.inducestatement · cited by 80
- SimpleGraph.Embeddingstatement · cited by 41
- Set.embeddingOfSubsetproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- SimpleGraph.induce_connected_of_patchesproof · cited by 2
- SimpleGraph.induceHomOfLE_toHomstatement · cited by 0
- SimpleGraph.induceHomOfLE_applystatement · cited by 0
- SimpleGraph.induceHomOfLE.congr_simpstatement and proof · cited by 0
- SimpleGraph.Walk.map_induce_induceHomOfLEstatement · cited by 0