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 original first-admission records.
Exact expanded first-order arithmetic statement
forall r s b c l x a m. (forall gcrt_solution_index_solution_last_source gcrt_solution_residue_solution_last_source gcrt_solution_modulus_solution_last_source. (exists ff_lt_gcrt_solution_last_source_bound. ff_lt_gcrt_solution_last_source_bound + S gcrt_solution_index_solution_last_source = S l) -> (((exists ff_h_gcrt_solution_last_source_residue. ff_h_gcrt_solution_last_source_residue + S (gcrt_solution_residue_solution_last_source) = S ((S (gcrt_solution_index_solution_last_source)) * s)) /\ exists ff_q_gcrt_solution_last_source_residue. r = ff_q_gcrt_solution_last_source_residue * S ((S (gcrt_solution_index_solution_last_source)) * s) + (gcrt_solution_residue_solution_last_source))) -> (((exists ff_h_gcrt_solution_last_source_modulus. ff_h_gcrt_solution_last_source_modulus + S (gcrt_solution_modulus_solution_last_source) = S ((S (gcrt_solution_index_solution_last_source)) * c)) /\ exists ff_q_gcrt_solution_last_source_modulus. b = ff_q_gcrt_solution_last_source_modulus * S ((S (gcrt_solution_index_solution_last_source)) * c) + (gcrt_solution_modulus_solution_last_source))) -> (exists hgcrt_mod_left_gcrt_solution_last_source_congruence hgcrt_mod_right_gcrt_solution_last_source_congruence. x + gcrt_solution_modulus_solution_last_source * hgcrt_mod_left_gcrt_solution_last_source_congruence = gcrt_solution_residue_solution_last_source + gcrt_solution_modulus_solution_last_source * hgcrt_mod_right_gcrt_solution_last_source_congruence)) -> (((exists ff_h_gcrt_solution_last_residue. ff_h_gcrt_solution_last_residue + S (a) = S ((S (l)) * s)) /\ exists ff_q_gcrt_solution_last_residue. r = ff_q_gcrt_solution_last_residue * S ((S (l)) * s) + (a))) -> (((exists ff_h_gcrt_solution_last_modulus. ff_h_gcrt_solution_last_modulus + S (m) = S ((S (l)) * c)) /\ exists ff_q_gcrt_solution_last_modulus. b = ff_q_gcrt_solution_last_modulus * S ((S (l)) * c) + (m))) -> (exists hgcrt_mod_left_gcrt_solution_last_result hgcrt_mod_right_gcrt_solution_last_result. x + m * hgcrt_mod_left_gcrt_solution_last_result = a + m * hgcrt_mod_right_gcrt_solution_last_result)Constructive proof overview
Generated structural guide
The last residue/modulus pair of a solved successor list satisfies its actual congruence.
The unchanged tactic script uses 1 declared prerequisite and contains 19 exact native proof lines.
Alpha v34 checked-use · first admitted v24 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
le_refl 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.
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–11
Work with arbitrary variables or the premises of the current implication.
- L11
intro hm
Original exact command ledger · 19 lines
Separate complete second-wave branches: Full G011 proof · Alpha v27.