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 p b c l. ~(p = 0) -> exists qb qc db dc. (forall fdp_index_lucas_digits. (exists gsp_lt_gap_lucas_digits_index_bound. gsp_lt_gap_lucas_digits_index_bound + S fdp_index_lucas_digits = l) -> exists fdp_value_lucas_digits fdp_quotient_lucas_digits fdp_remainder_lucas_digits. (((exists ff_h_fdp_lucas_digits_source. ff_h_fdp_lucas_digits_source + S (fdp_value_lucas_digits) = S ((S (fdp_index_lucas_digits)) * c)) /\ exists ff_q_fdp_lucas_digits_source. b = ff_q_fdp_lucas_digits_source * S ((S (fdp_index_lucas_digits)) * c) + (fdp_value_lucas_digits))) /\ ((((exists ff_h_fdp_lucas_digits_quotient_entry. ff_h_fdp_lucas_digits_quotient_entry + S (fdp_quotient_lucas_digits) = S ((S (fdp_index_lucas_digits)) * qc)) /\ exists ff_q_fdp_lucas_digits_quotient_entry. qb = ff_q_fdp_lucas_digits_quotient_entry * S ((S (fdp_index_lucas_digits)) * qc) + (fdp_quotient_lucas_digits))) /\ ((((exists ff_h_fdp_lucas_digits_remainder_entry. ff_h_fdp_lucas_digits_remainder_entry + S (fdp_remainder_lucas_digits) = S ((S (fdp_index_lucas_digits)) * dc)) /\ exists ff_q_fdp_lucas_digits_remainder_entry. db = ff_q_fdp_lucas_digits_remainder_entry * S ((S (fdp_index_lucas_digits)) * dc) + (fdp_remainder_lucas_digits))) /\ (fdp_value_lucas_digits = p * fdp_quotient_lucas_digits + fdp_remainder_lucas_digits /\ (exists gsp_lt_gap_lucas_digits_remainder_bound. gsp_lt_gap_lucas_digits_remainder_bound + S fdp_remainder_lucas_digits = p)))))Constructive proof overview
Generated structural guide
Every finite beta-coded natural prefix has actual beta-coded quotient and least-significant digit prefixes for each nonzero base.
The unchanged tactic script uses 1 declared prerequisite and contains 11 exact native proof lines.
dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged
Proof neighborhood
Direct dependencies
beta_division_prefix_exists Alpha 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 dependency-curried candidate body does not grant checked theorem use 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 assumptionsL1–5
02Use earlier factsL6–11
Instantiate or apply named facts and discharge the corresponding proof obligations.