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f0f05de | 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 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | import OAI.Combinatorics.BalancedRyser.Local.LocalConditionFibers
namespace OAI
namespace Balanced.Local.ConditionSpec
noncomputable section
open scoped Classical
open LocalFiberBounds
variable {F : Type*} [Field F] [Fintype F] [DecidableEq F]
variable {b κ : ℕ}
theorem indexedThrough_eq_of_unused_eq (a : DirectionAssignment F b κ)
(M N : MergedPairs F)
(h : ∀ d, d ∉ FourEvents.usedDirections a → M d = N d)
(p : Point F) :
indexedThrough M (unusedDirections a) p =
indexedThrough N (unusedDirections a) p := by
ext ds
by_cases hd : ds.1 ∉ FourEvents.usedDirections a
· simp [indexedThrough, unusedDirections, hd, constituent, h ds.1 hd]
· simp [indexedThrough, unusedDirections, hd]
theorem pointHolds_iff_of_unused_eq (a : DirectionAssignment F b κ)
(p : Point F) (M N : MergedPairs F)
(h : ∀ d, d ∉ FourEvents.usedDirections a → M d = N d)
(x : Position b → Point F) (v : Position b) (z : Code b κ) :
PointHolds a p M x v z ↔ PointHolds a p N x v z := by
rcases z with z | xy | w | cw
· simp only [PointHolds]
apply exists_congr
intro d
by_cases hd : d ∉ FourEvents.usedDirections a
· simp only [hd, constituent, h d hd]
· simp only [hd, false_and]
· rfl
· simp only [PointHolds]
apply exists_congr
intro d
by_cases hd : d ∉ FourEvents.usedDirections a
· simp only [hd, mergedPoints, constituent, h d hd]
· simp only [hd, false_and]
· rfl
theorem holds_iff_pointHolds_of_unused_eq (P : EqualityPattern b κ)
(a : DirectionAssignment F b κ) (bits : Bits b) (p : Point F)
(M N : MergedPairs F)
(h : ∀ d, d ∉ FourEvents.usedDirections a → M d = N d)
(v : Position b) (z : Code b κ) :
Holds P a bits p M v z ↔
PointHolds a p N (prescribedPoint P a bits M) v z := by
rw [holds_eq_pointHolds]
exact pointHolds_iff_of_unused_eq a p M N h _ v z
end
end Balanced.Local.ConditionSpec
end OAI
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