Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
Exact expanded first-order arithmetic statement
forall b c l a. (forall ftsf_index_drop_next ftsf_factor_drop_next. (exists ftsf_gap_drop_next_bound. ftsf_gap_drop_next_bound + S ftsf_index_drop_next = (S l)) -> (((exists ff_h_ftsf_drop_next_entry. ff_h_ftsf_drop_next_entry + S (ftsf_factor_drop_next) = S ((S (ftsf_index_drop_next)) * c)) /\ exists ff_q_ftsf_drop_next_entry. b = ff_q_ftsf_drop_next_entry * S ((S (ftsf_index_drop_next)) * c) + (ftsf_factor_drop_next))) -> (exists ftsf_first_drop_next_representation ftsf_second_drop_next_representation. (ftsf_factor_drop_next) = ftsf_first_drop_next_representation * ftsf_first_drop_next_representation + ftsf_second_drop_next_representation * ftsf_second_drop_next_representation)) -> (((exists ff_h_ftsf_last_entry. ff_h_ftsf_last_entry + S (a) = S ((S (l)) * c)) /\ exists ff_q_ftsf_last_entry. b = ff_q_ftsf_last_entry * S ((S (l)) * c) + (a))) -> (exists ftsf_first_last_result ftsf_second_last_result. (a) = ftsf_first_last_result * ftsf_first_last_result + ftsf_second_last_result * ftsf_second_last_result)Constructive proof overview
Generated structural guide
The final decoded factor of a represented successor prefix has its own explicit two-square witnesses.
The unchanged tactic script uses 1 declared prerequisite and contains 12 exact native proof lines.
Alpha v34 checked-use · first admitted v23 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
le_refl Stable theorem; checked-use authorizedDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.