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e320e82 | 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 | import Mathlib
import OAI.Combinatorics.IndependentSets.Encoding.GeometryExpr
namespace OAI
namespace LargeIndependentSets.GeometryNames
open IndependentSetsCut.CounterMachine UniformLC
open scoped Classical
noncomputable section
variable (L R : Type) [Fintype L] [Fintype R] (n D : ℕ) [NeZero D]
def pointEquiv : StaticPoint L R n D ≃ Fin (staticCount L R n D) :=
Fintype.equivFin (StaticPoint L R n D)
lemma nodeEquiv_val {nu nv : ℕ} (x : Node L R n D nu nv) :
(nodeEquiv L R n D nu nv x).val=
(pointEquiv L R n D x.2).val+staticCount L R n D*
((finFunctionFinEquiv x.1.2).val+nv^n*(finFunctionFinEquiv x.1.1).val) := rfl
def pointLookup (f : StaticPoint L R n D → ℕ) (x : Expr) : Expr :=
Expr.finLookup (fun i => f ((pointEquiv L R n D).symm i)) x
lemma pointLookup_eval (f : StaticPoint L R n D → ℕ) (x : Expr) (s : List Bool) (a : ℕ → ℕ)
(v : StaticPoint L R n D) (hv : x.eval s a=(pointEquiv L R n D v).val) :
(pointLookup L R n D f x).eval s a=f v := by
rw [pointLookup,Expr.finLookup_eval _ _ _ _ (pointEquiv L R n D v) hv,Equiv.symm_apply_apply]
lemma pointExpr_code (t : Table L R) (x : Expr) (a : ℕ → ℕ) (i : Fin (size L R n D t))
(hi : x.eval t.bits a=i.val) :
(pointExpr L R n D x).eval t.bits a=
(pointEquiv L R n D ((nodeEquiv L R n D t.nu t.nv).symm i).2).val :=
pointExpr_eval L R n D t x a i hi
end
end LargeIndependentSets.GeometryNames
end OAI
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