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 expanded first-order arithmetic statement
forall m b c l. (forall eu_factor_index_factors_drop_old. (exists eut_gap_eu_factors_drop_old_index. eut_gap_eu_factors_drop_old_index + S (eu_factor_index_factors_drop_old) = (S l)) -> exists eu_factor_value_factors_drop_old. (((exists fs_h_eu_factors_drop_old_at. fs_h_eu_factors_drop_old_at + S (eu_factor_value_factors_drop_old) = S ((S (eu_factor_index_factors_drop_old)) * c)) /\ exists fs_q_eu_factors_drop_old_at. b = fs_q_eu_factors_drop_old_at * S ((S (eu_factor_index_factors_drop_old)) * c) + (eu_factor_value_factors_drop_old))) /\ ((((forall eut_divisor_eu_factors_drop_old_choice_coprime. (exists eut_left_eu_factors_drop_old_choice_coprime. (eu_factor_index_factors_drop_old) = eut_divisor_eu_factors_drop_old_choice_coprime * eut_left_eu_factors_drop_old_choice_coprime) -> (exists eut_right_eu_factors_drop_old_choice_coprime. (m) = eut_divisor_eu_factors_drop_old_choice_coprime * eut_right_eu_factors_drop_old_choice_coprime) -> eut_divisor_eu_factors_drop_old_choice_coprime = 1) /\ (eu_factor_value_factors_drop_old)=(eu_factor_index_factors_drop_old)) \/ (~(forall eut_divisor_eu_factors_drop_old_choice_coprime. (exists eut_left_eu_factors_drop_old_choice_coprime. (eu_factor_index_factors_drop_old) = eut_divisor_eu_factors_drop_old_choice_coprime * eut_left_eu_factors_drop_old_choice_coprime) -> (exists eut_right_eu_factors_drop_old_choice_coprime. (m) = eut_divisor_eu_factors_drop_old_choice_coprime * eut_right_eu_factors_drop_old_choice_coprime) -> eut_divisor_eu_factors_drop_old_choice_coprime = 1) /\ (eu_factor_value_factors_drop_old)=1)))) -> (forall eu_factor_index_factors_drop_new. (exists eut_gap_eu_factors_drop_new_index. eut_gap_eu_factors_drop_new_index + S (eu_factor_index_factors_drop_new) = (l)) -> exists eu_factor_value_factors_drop_new. (((exists fs_h_eu_factors_drop_new_at. fs_h_eu_factors_drop_new_at + S (eu_factor_value_factors_drop_new) = S ((S (eu_factor_index_factors_drop_new)) * c)) /\ exists fs_q_eu_factors_drop_new_at. b = fs_q_eu_factors_drop_new_at * S ((S (eu_factor_index_factors_drop_new)) * c) + (eu_factor_value_factors_drop_new))) /\ ((((forall eut_divisor_eu_factors_drop_new_choice_coprime. (exists eut_left_eu_factors_drop_new_choice_coprime. (eu_factor_index_factors_drop_new) = eut_divisor_eu_factors_drop_new_choice_coprime * eut_left_eu_factors_drop_new_choice_coprime) -> (exists eut_right_eu_factors_drop_new_choice_coprime. (m) = eut_divisor_eu_factors_drop_new_choice_coprime * eut_right_eu_factors_drop_new_choice_coprime) -> eut_divisor_eu_factors_drop_new_choice_coprime = 1) /\ (eu_factor_value_factors_drop_new)=(eu_factor_index_factors_drop_new)) \/ (~(forall eut_divisor_eu_factors_drop_new_choice_coprime. (exists eut_left_eu_factors_drop_new_choice_coprime. (eu_factor_index_factors_drop_new) = eut_divisor_eu_factors_drop_new_choice_coprime * eut_left_eu_factors_drop_new_choice_coprime) -> (exists eut_right_eu_factors_drop_new_choice_coprime. (m) = eut_divisor_eu_factors_drop_new_choice_coprime * eut_right_eu_factors_drop_new_choice_coprime) -> eut_divisor_eu_factors_drop_new_choice_coprime = 1) /\ (eu_factor_value_factors_drop_new)=1))))Constructive proof overview
Generated structural guide
Restrict an actual weighted-factor prefix to its predecessor interval.
The unchanged tactic script uses 1 declared prerequisite and contains 13 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · 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.