Finset card gt of interpolate degree ge
KZG.CommitmentScheme.finset_card_gt_of_interpolate_degree_ge
Plain-language statement
A high interpolation degree forces the interpolation set to have more than n + 1 points.
Exact Lean statement
lemma finset_card_gt_of_interpolate_degree_ge {n L : ℕ} (S : Finset (Fin L))
(queryOf : Fin L → ZMod p) (responseOf : Fin L → ZMod p)
(hquery : Set.InjOn queryOf ↑S)
(hS_deg : (↑(n + 1) : WithBot ℕ) ≤
(CLagrange.interpolate S queryOf responseOf).degree) :
n + 1 < S.cardFormal artifact
Lean source
lemma finset_card_gt_of_interpolate_degree_ge {n L : ℕ} (S : Finset (Fin L)) (queryOf : Fin L → ZMod p) (responseOf : Fin L → ZMod p) (hquery : Set.InjOn queryOf ↑S) (hS_deg : (↑(n + 1) : WithBot ℕ) ≤ (CLagrange.interpolate S queryOf responseOf).degree) : n + 1 < S.card := by have h_lt := Lagrange.degree_interpolate_lt responseOf hquery have h_ge : (↑(n + 1) : WithBot ℕ) ≤ (Lagrange.interpolate S queryOf responseOf).degree := by have h := hS_deg rwa [show (CLagrange.interpolate S queryOf responseOf).degree = (Lagrange.interpolate S queryOf responseOf).degree from by rw [← CLagrange.cinterpolate_eq_interpolate, ← degree_toPoly]] at h have h_card_gt : (↑(n + 1) : WithBot ℕ) < (S.card : WithBot ℕ) := lt_of_le_of_lt h_ge h_lt exact_mod_cast h_card_gt- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/Commitments/Functional/KZG/FunctionBinding/DegreeConflict.lean:147-169
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Person-level attribution pending.
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Source project: ArkLib
Person-level attribution pending.
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Plain-language statement
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Source project: ArkLib
Person-level attribution pending.