Exact expanded first-order arithmetic statement
forall p n m r. (exists pfa_offset_left_transport pfa_offset_right_transport. (n) + (p) * pfa_offset_left_transport = (m) + (p) * pfa_offset_right_transport) -> (((exists pfa_gap_transport_sourcebound. pfa_gap_transport_sourcebound + S (r) = (p)) /\ ((exists pfa_offset_left_transport_sourcecongruence pfa_offset_right_transport_sourcecongruence. (m) + (p) * pfa_offset_left_transport_sourcecongruence = (r) + (p) * pfa_offset_right_transport_sourcecongruence)))) -> (((exists pfa_gap_transport_resultbound. pfa_gap_transport_resultbound + S (r) = (p)) /\ ((exists pfa_offset_left_transport_resultcongruence pfa_offset_right_transport_resultcongruence. (n) + (p) * pfa_offset_left_transport_resultcongruence = (r) + (p) * pfa_offset_right_transport_resultcongruence))))Constructive proof overview
Generated structural guide
Balanced congruence transports canonical residues; no quotient oracle is assumed.
The unchanged tactic script uses 1 declared prerequisite and contains 16 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.