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.
Public research checkpoint: original HA and independently compiled Lean verified; not Alpha-enrolled, no Alpha checked-use authority; not Stable
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. The literal dependency-closed bundle is checked by original HA and the independently compiled Lean verifier. Public delivery grants no Alpha checked-use authority or 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.