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 a p. (exists bcf_lt_gap_bpc_chain_terminal. bcf_lt_gap_bpc_chain_terminal + S (1) = a) -> ((((~(p = 1) /\ forall frm_prime_left_bpc_next_prime frm_prime_right_bpc_next_prime. p = frm_prime_left_bpc_next_prime * frm_prime_right_bpc_next_prime -> frm_prime_left_bpc_next_prime = 1 \/ frm_prime_right_bpc_next_prime = 1)) /\ ((exists bcf_lt_gap_bpc_next_lower. bcf_lt_gap_bpc_next_lower + S (a) = p) /\ (exists bcf_lt_gap_bpc_next_upper. bcf_lt_gap_bpc_next_upper + S (p) = a + a)))) -> (exists bcf_lt_gap_bpc_chain_next. bcf_lt_gap_bpc_chain_next + S (1) = p)Constructive proof overview
Generated structural guide
Every strict Bertrand successor preserves the initial 1<n domain guard.
The unchanged tactic script uses 1 declared prerequisite and contains 12 exact native proof lines.
Alpha v34 checked-use · first admitted v20 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
lt_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.
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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.