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 d. (forall ppf_index_common_successor ppf_entry_common_successor. (exists pvs_gap_common_successorbound. pvs_gap_common_successorbound + S (ppf_index_common_successor) = (S l)) -> (((exists ff_h_pvs_common_successorentry. ff_h_pvs_common_successorentry + S (ppf_entry_common_successor) = S ((S (ppf_index_common_successor)) * c)) /\ exists ff_q_pvs_common_successorentry. b = ff_q_pvs_common_successorentry * S ((S (ppf_index_common_successor)) * c) + (ppf_entry_common_successor))) -> (exists pvs_factor_common_successordivisor. (ppf_entry_common_successor) = (d) * pvs_factor_common_successordivisor)) -> (forall ppf_index_common_previous ppf_entry_common_previous. (exists pvs_gap_common_previousbound. pvs_gap_common_previousbound + S (ppf_index_common_previous) = (l)) -> (((exists ff_h_pvs_common_previousentry. ff_h_pvs_common_previousentry + S (ppf_entry_common_previous) = S ((S (ppf_index_common_previous)) * c)) /\ exists ff_q_pvs_common_previousentry. b = ff_q_pvs_common_previousentry * S ((S (ppf_index_common_previous)) * c) + (ppf_entry_common_previous))) -> (exists pvs_factor_common_previousdivisor. (ppf_entry_common_previous) = (d) * pvs_factor_common_previousdivisor))Constructive proof overview
Generated structural guide
A common divisor of a successor beta prefix divides every entry of its predecessor.
The unchanged tactic script uses 1 declared prerequisite and contains 17 exact native proof lines.
Alpha v34 checked-use · first admitted v29 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
le_succ 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.