| import Mathlib | |
| namespace OAI | |
| /-! Finite-index virtual isomorphism graphs. -/ | |
| namespace ArithmeticGerms | |
| variable {G H : Type*} [Group G] [Group H] | |
| structure VirtualGraph (G H : Type*) [Group G] [Group H] where | |
| graph : Subgroup (G × H) | |
| fst_injective : Function.Injective ((MonoidHom.fst G H).comp graph.subtype) | |
| snd_injective : Function.Injective ((MonoidHom.snd G H).comp graph.subtype) | |
| fst_finite : (graph.map (MonoidHom.fst G H)).FiniteIndex | |
| snd_finite : (graph.map (MonoidHom.snd G H)).FiniteIndex | |
| attribute [instance] VirtualGraph.fst_finite VirtualGraph.snd_finite | |
| namespace VirtualGraph | |
| variable (C : VirtualGraph G H) | |
| @[ext] | |
| theorem ext {C D : VirtualGraph G H} (h : C.graph = D.graph) : C = D := by | |
| cases C | |
| cases D | |
| cases h | |
| rfl | |
| abbrev domain : Subgroup G := C.graph.map (MonoidHom.fst G H) | |
| abbrev codomain : Subgroup H := C.graph.map (MonoidHom.snd G H) | |
| end VirtualGraph | |
| end ArithmeticGerms | |
| end OAI | |