| import Mathlib | |
| import OAI.Probability.CriticalPercolation.GraphGeometry.UniformGeometry | |
| namespace OAI | |
| section | |
| section | |
| noncomputable section | |
| open Set Function | |
| open scoped Classical | |
| namespace CriticalPercolation.BondGraph | |
| variable {V E : Type*} (G : BondGraph V E) | |
| @[ext] lemma Aut.ext {f g : G.Aut} (hv : f.vertex=g.vertex) (he : f.edge=g.edge) : f=g := by | |
| cases f | |
| cases g | |
| cases hv | |
| cases he | |
| rfl | |
| instance : Group G.Aut where | |
| one := ⟨Equiv.refl V,Equiv.refl E,by intro e; simp⟩ | |
| mul f g := Aut.trans G g f | |
| inv f := Aut.symm G f | |
| mul_assoc f g h := by apply Aut.ext G <;> rfl | |
| one_mul f := by apply Aut.ext G <;> rfl | |
| mul_one f := by apply Aut.ext G <;> rfl | |
| inv_mul_cancel f := by | |
| apply Aut.ext G <;> apply Equiv.ext <;> intro x <;> | |
| exact Equiv.symm_apply_apply _ x | |
| instance : MulAction G.Aut V where | |
| smul f x := f.vertex x | |
| one_smul _ := rfl | |
| mul_smul _ _ _ := rfl | |
| @[simp] lemma Aut.smul_vertex (f : G.Aut) (x : V) : f • x=f.vertex x := rfl | |
| end CriticalPercolation.BondGraph | |
| end | |
| end | |
| end | |
| end OAI | |