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f205175 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | 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
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