{"id":"e-ec99adce3b0da943","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-f7a8eb403cd4bd0f","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":"a5a249b0bc2fd04e4253d9f34aed477786f576beb65d84e95e86faffff27414e","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":28126,"certificate_compressed_size":5041,"conclusion_name":"shift_x_plus_one of Triangle read by rows: T(n,k) is the number of ternary words (i.e., finite sequences of 0's, 1's and 2's) of length n having k occurrences of 01's (0 <= k <= floor(n/2)).","claims":[],"premises":[],"cited_by":[]}