Exact expanded first-order arithmetic statement
forall p b c a l. (exists pfa_gap_constant_bound. pfa_gap_constant_bound + S (a) = (p)) -> (forall pfp_repeat_index_constant_repeat. (exists pfa_gap_constant_repeatindex. pfa_gap_constant_repeatindex + S (pfp_repeat_index_constant_repeat) = (l)) -> (((exists ff_h_pfp_constant_repeatentry. ff_h_pfp_constant_repeatentry + S (a) = S ((S (pfp_repeat_index_constant_repeat)) * c)) /\ exists ff_q_pfp_constant_repeatentry. b = ff_q_pfp_constant_repeatentry * S ((S (pfp_repeat_index_constant_repeat)) * c) + (a)))) -> (forall fom_index_pfp_constant_result. (exists fom_gap_pfp_constant_result_index_bound. fom_gap_pfp_constant_result_index_bound + S (fom_index_pfp_constant_result) = l) -> exists fom_value_pfp_constant_result. ((((exists fom_beta_height_pfp_constant_result_entry. fom_beta_height_pfp_constant_result_entry + S (fom_value_pfp_constant_result) = S ((S (fom_index_pfp_constant_result)) * c)) /\ exists fom_beta_quotient_pfp_constant_result_entry. b = fom_beta_quotient_pfp_constant_result_entry * S ((S (fom_index_pfp_constant_result)) * c) + (fom_value_pfp_constant_result))) /\ (exists fom_gap_pfp_constant_result_value_bound. fom_gap_pfp_constant_result_value_bound + S (fom_value_pfp_constant_result) = p)))Constructive proof overview
Generated structural guide
A genuinely repeated canonical value forms a bounded coefficient table, including length zero.
The unchanged tactic script uses 0 declared prerequisites and contains 15 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.