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 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.
Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
mod_eq_trans 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.