Sumcheck round Poly degree LE
Sumcheck.Spec.SingleRound.sumcheck_roundPoly_degreeLE
Project documentation
Auxiliary lemma for proving that the polynomial sent by the honest prover is of degree at most deg
Exact Lean statement
theorem sumcheck_roundPoly_degreeLE (i : Fin (n + 1)) {challenges : Fin i.castSucc → R}
{poly : R[X Fin (n + 1)]} (hp : poly ∈ R⦃≤ deg⦄[X Fin (n + 1)]) :
∑ x ∈ (univ.map D) ^ᶠ (n - i), poly ⸨X ⦃i⦄, challenges, x⸩'
(by simp; omega) ∈ R⦃≤ deg⦄[X]Formal artifact
Lean source
theorem sumcheck_roundPoly_degreeLE (i : Fin (n + 1)) {challenges : Fin i.castSucc → R} {poly : R[X Fin (n + 1)]} (hp : poly ∈ R⦃≤ deg⦄[X Fin (n + 1)]) : ∑ x ∈ (univ.map D) ^ᶠ (n - i), poly ⸨X ⦃i⦄, challenges, x⸩' (by simp; omega) ∈ R⦃≤ deg⦄[X] := by refine mem_degreeLE.mpr (le_trans (degree_sum_le ((univ.map D) ^ᶠ (n - i)) _) ?_) simp only [Finset.sup_le_iff, Fintype.mem_piFinset, mem_map, mem_univ, true_and] intro x hx refine le_trans (degree_map_le) (natDegree_le_iff_degree_le.mp ?_) rw [natDegree_finSuccEquivNth] exact degreeOf_le_iff.mpr fun m a ↦ hp a i- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/ProofSystem/Sumcheck/Spec/SingleRound.lean:787-796
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Person-level attribution pending.
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Source project: ArkLib
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