Selected-floor prefix certificate

Proved

D1Bound5.pairLightSelectedFloorPrefixBool_add

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

the selected-floor certificate succeeds for at most (m+n) head rows of the supplied cached vertex list. Each selected head is checked against its complete remaining tail, including vertices beyond the end of this chunk. The quadratic coordinate parameters are τ = tau and ν = nu, and the sieve is sieve. Concatenate two finite head prefixes without shortening any head's tail. The identity also covers malformed and unequal witness lists.

Preamble

import Init
import Mathlib.Data.List.Basic
import Definitions.Def_D1Bound5_PairLightArithmeticChunks_Definitions
import Definitions.Def_D1Bound5_PairLightArithmetic_Definitions

Formal statement

section
namespace D1Bound5


theorem _root_.D1Bound5.pairLightSelectedFloorPrefixBool_add
    (tau nu : Int) (sieve : List (Nat × Nat)) (m n : Nat)
    (cached : List PairLightCachedVertex) (rows : List (Nat × List Nat)) :
    pairLightSelectedFloorPrefixBool tau nu sieve (m+n) cached rows =
      (pairLightSelectedFloorPrefixBool tau nu sieve m cached rows &&
        pairLightSelectedFloorPrefixBool tau nu sieve n (cached.drop m) (rows.drop m)) := by sorry



end D1Bound5
end

Source

D1Bound5/PairLightArithmeticPrefixConcat.lean, lines 5-33, SHA-256 2a00628c416022cc78732a0b0067542b89f738f591b1289ce4370ba3279d0d3b. Project: https://github.com/tomislav-math/d1-bound5-lean

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