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
(((0) = 0 /\ (1) = 1) \/ exists ff_exponent_bl_zero ff_lower_bl_zero ff_upper_bl_zero. (((1) = S ff_exponent_bl_zero) /\ ((exists ff_positive_bl_zero. ff_positive_bl_zero + 1 = (0)) /\ ((exists pa_b_bl_zero_lower pa_c_bl_zero_lower. ((forall pa_i_bl_zero_lower_repeat. (exists pa_lt_bl_zero_lower_repeat_bound. pa_lt_bl_zero_lower_repeat_bound + S pa_i_bl_zero_lower_repeat = ff_exponent_bl_zero) -> (((exists pa_h_bl_zero_lower_repeat_decoded. pa_h_bl_zero_lower_repeat_decoded + S (2) = S ((S (pa_i_bl_zero_lower_repeat)) * pa_c_bl_zero_lower)) /\ exists pa_q_bl_zero_lower_repeat_decoded. pa_b_bl_zero_lower = pa_q_bl_zero_lower_repeat_decoded * S ((S (pa_i_bl_zero_lower_repeat)) * pa_c_bl_zero_lower) + (2)))) /\ (exists pa_u_bl_zero_lower_product pa_v_bl_zero_lower_product. ((((exists pa_h_bl_zero_lower_product_start. pa_h_bl_zero_lower_product_start + S (1) = S ((S (0)) * pa_v_bl_zero_lower_product)) /\ exists pa_q_bl_zero_lower_product_start. pa_u_bl_zero_lower_product = pa_q_bl_zero_lower_product_start * S ((S (0)) * pa_v_bl_zero_lower_product) + (1))) /\ ((((exists pa_h_bl_zero_lower_product_terminal. pa_h_bl_zero_lower_product_terminal + S (ff_lower_bl_zero) = S ((S (ff_exponent_bl_zero)) * pa_v_bl_zero_lower_product)) /\ exists pa_q_bl_zero_lower_product_terminal. pa_u_bl_zero_lower_product = pa_q_bl_zero_lower_product_terminal * S ((S (ff_exponent_bl_zero)) * pa_v_bl_zero_lower_product) + (ff_lower_bl_zero))) /\ forall pa_i_bl_zero_lower_product. (exists pa_lt_bl_zero_lower_product_bound. pa_lt_bl_zero_lower_product_bound + S pa_i_bl_zero_lower_product = ff_exponent_bl_zero) -> exists pa_p_bl_zero_lower_product pa_r_bl_zero_lower_product pa_s_bl_zero_lower_product. ((((exists pa_h_bl_zero_lower_product_factor. pa_h_bl_zero_lower_product_factor + S (pa_p_bl_zero_lower_product) = S ((S (pa_i_bl_zero_lower_product)) * pa_c_bl_zero_lower)) /\ exists pa_q_bl_zero_lower_product_factor. pa_b_bl_zero_lower = pa_q_bl_zero_lower_product_factor * S ((S (pa_i_bl_zero_lower_product)) * pa_c_bl_zero_lower) + (pa_p_bl_zero_lower_product))) /\ ((((exists pa_h_bl_zero_lower_product_partial. pa_h_bl_zero_lower_product_partial + S (pa_r_bl_zero_lower_product) = S ((S (pa_i_bl_zero_lower_product)) * pa_v_bl_zero_lower_product)) /\ exists pa_q_bl_zero_lower_product_partial. pa_u_bl_zero_lower_product = pa_q_bl_zero_lower_product_partial * S ((S (pa_i_bl_zero_lower_product)) * pa_v_bl_zero_lower_product) + (pa_r_bl_zero_lower_product))) /\ ((((exists pa_h_bl_zero_lower_product_successor. pa_h_bl_zero_lower_product_successor + S (pa_s_bl_zero_lower_product) = S ((S (S pa_i_bl_zero_lower_product)) * pa_v_bl_zero_lower_product)) /\ exists pa_q_bl_zero_lower_product_successor. pa_u_bl_zero_lower_product = pa_q_bl_zero_lower_product_successor * S ((S (S pa_i_bl_zero_lower_product)) * pa_v_bl_zero_lower_product) + (pa_s_bl_zero_lower_product))) /\ pa_s_bl_zero_lower_product = pa_r_bl_zero_lower_product * pa_p_bl_zero_lower_product)))))))) /\ ((exists pa_b_bl_zero_upper pa_c_bl_zero_upper. ((forall pa_i_bl_zero_upper_repeat. (exists pa_lt_bl_zero_upper_repeat_bound. pa_lt_bl_zero_upper_repeat_bound + S pa_i_bl_zero_upper_repeat = 1) -> (((exists pa_h_bl_zero_upper_repeat_decoded. pa_h_bl_zero_upper_repeat_decoded + S (2) = S ((S (pa_i_bl_zero_upper_repeat)) * pa_c_bl_zero_upper)) /\ exists pa_q_bl_zero_upper_repeat_decoded. pa_b_bl_zero_upper = pa_q_bl_zero_upper_repeat_decoded * S ((S (pa_i_bl_zero_upper_repeat)) * pa_c_bl_zero_upper) + (2)))) /\ (exists pa_u_bl_zero_upper_product pa_v_bl_zero_upper_product. ((((exists pa_h_bl_zero_upper_product_start. pa_h_bl_zero_upper_product_start + S (1) = S ((S (0)) * pa_v_bl_zero_upper_product)) /\ exists pa_q_bl_zero_upper_product_start. pa_u_bl_zero_upper_product = pa_q_bl_zero_upper_product_start * S ((S (0)) * pa_v_bl_zero_upper_product) + (1))) /\ ((((exists pa_h_bl_zero_upper_product_terminal. pa_h_bl_zero_upper_product_terminal + S (ff_upper_bl_zero) = S ((S (1)) * pa_v_bl_zero_upper_product)) /\ exists pa_q_bl_zero_upper_product_terminal. pa_u_bl_zero_upper_product = pa_q_bl_zero_upper_product_terminal * S ((S (1)) * pa_v_bl_zero_upper_product) + (ff_upper_bl_zero))) /\ forall pa_i_bl_zero_upper_product. (exists pa_lt_bl_zero_upper_product_bound. pa_lt_bl_zero_upper_product_bound + S pa_i_bl_zero_upper_product = 1) -> exists pa_p_bl_zero_upper_product pa_r_bl_zero_upper_product pa_s_bl_zero_upper_product. ((((exists pa_h_bl_zero_upper_product_factor. pa_h_bl_zero_upper_product_factor + S (pa_p_bl_zero_upper_product) = S ((S (pa_i_bl_zero_upper_product)) * pa_c_bl_zero_upper)) /\ exists pa_q_bl_zero_upper_product_factor. pa_b_bl_zero_upper = pa_q_bl_zero_upper_product_factor * S ((S (pa_i_bl_zero_upper_product)) * pa_c_bl_zero_upper) + (pa_p_bl_zero_upper_product))) /\ ((((exists pa_h_bl_zero_upper_product_partial. pa_h_bl_zero_upper_product_partial + S (pa_r_bl_zero_upper_product) = S ((S (pa_i_bl_zero_upper_product)) * pa_v_bl_zero_upper_product)) /\ exists pa_q_bl_zero_upper_product_partial. pa_u_bl_zero_upper_product = pa_q_bl_zero_upper_product_partial * S ((S (pa_i_bl_zero_upper_product)) * pa_v_bl_zero_upper_product) + (pa_r_bl_zero_upper_product))) /\ ((((exists pa_h_bl_zero_upper_product_successor. pa_h_bl_zero_upper_product_successor + S (pa_s_bl_zero_upper_product) = S ((S (S pa_i_bl_zero_upper_product)) * pa_v_bl_zero_upper_product)) /\ exists pa_q_bl_zero_upper_product_successor. pa_u_bl_zero_upper_product = pa_q_bl_zero_upper_product_successor * S ((S (S pa_i_bl_zero_upper_product)) * pa_v_bl_zero_upper_product) + (pa_s_bl_zero_upper_product))) /\ pa_s_bl_zero_upper_product = pa_r_bl_zero_upper_product * pa_p_bl_zero_upper_product)))))))) /\ ((exists ff_lower_gap_bl_zero. ff_lower_gap_bl_zero + (ff_lower_bl_zero) = (0)) /\ (exists ff_upper_gap_bl_zero. ff_upper_gap_bl_zero + S (0) = (ff_upper_bl_zero))))))))Constructive proof overview
Generated structural guide
The blueprint convention gives zero exactly one displayed binary digit.
The unchanged tactic script uses 0 declared prerequisites and contains 4 exact native proof lines.
Alpha v34 checked-use · first admitted v22 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
none
Direct 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.