Theorems · Theorem · combinatorics
SimpleGraph.induceHom_injective
∀ {V : Type u_1} {W : Type u_2} {G : SimpleGraph V} {G' : SimpleGraph W} {s : Set V} {t : Set W} (φ : G →g G')
(φst : Set.MapsTo (⇑φ) s t), Set.InjOn (⇑φ) s → Function.Injective ⇑(SimpleGraph.induceHom φ φst)- Defined in
- Mathlib.Combinatorics.SimpleGraph.Maps
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement · cited by 1,346
- Set.MapsTostatement and proof · cited by 732
- Set.InjOnstatement and proof · cited by 543
- SimpleGraph.Homstatement and proof · cited by 139
- SimpleGraph.inducestatement · cited by 80
- SimpleGraph.induceHomstatement · cited by 7
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