Exact expanded first-order arithmetic statement
forall p a. (exists pfa_gap_reflexive_bound. pfa_gap_reflexive_bound + S (a) = (p)) -> (((exists pfa_gap_reflexivebound. pfa_gap_reflexivebound + S (a) = (p)) /\ ((exists pfa_offset_left_reflexivecongruence pfa_offset_right_reflexivecongruence. (a) + (p) * pfa_offset_left_reflexivecongruence = (a) + (p) * pfa_offset_right_reflexivecongruence))))Constructive proof overview
Generated structural guide
Every bounded representative represents itself, including zero.
The unchanged tactic script uses 1 declared prerequisite and contains 8 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.
01Fix variables and assumptionsL1–3
02Separate the logical casesL4–4
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L4
split