{"id":"e-7b640b1203ef46c2","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-344301f9723c6726","premise_count":0,"theorem":"all-index identity Q_n = P_n certified by exact Ore-algebra division and identifying rows (polytool preserver-image certificate of the identity map)","lean_route":null,"lean_declarations":[],"certificate_hash":"9b862cae7d1fcc574cfdb3619d1c4be81b6650907a3b74abef6e321df87ab1e2","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":11719,"certificate_compressed_size":3143,"conclusion_name":"shift_x_plus_one of basis_map_A013609 of Triangle read by rows: T(n,k) is the number of lattice paths from (0,0) to (n,n) using steps E=(1,0), N=(0,1) and D=(1,1) (i.e., bilateral Schroeder paths), having k D=(1,1) steps.","claims":[],"premises":[],"cited_by":[]}