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 k. (exists pc_code_count_zero_source pc_scale_count_zero_source. (forall pc_index_count_zero_source_mask. (exists pc_lt_count_zero_source_mask_bound. pc_lt_count_zero_source_mask_bound + S (pc_index_count_zero_source_mask) = (0)) -> exists pc_bit_count_zero_source_mask. (((exists fs_h_pc_count_zero_source_mask_entry. fs_h_pc_count_zero_source_mask_entry + S (pc_bit_count_zero_source_mask) = S ((S (pc_index_count_zero_source_mask)) * pc_scale_count_zero_source)) /\ exists fs_q_pc_count_zero_source_mask_entry. pc_code_count_zero_source = fs_q_pc_count_zero_source_mask_entry * S ((S (pc_index_count_zero_source_mask)) * pc_scale_count_zero_source) + (pc_bit_count_zero_source_mask))) /\ (((((~(S (pc_index_count_zero_source_mask) = 1) /\ forall bpr_left_pc_count_zero_source_mask_choice_prime bpr_right_pc_count_zero_source_mask_choice_prime. S (pc_index_count_zero_source_mask) = bpr_left_pc_count_zero_source_mask_choice_prime * bpr_right_pc_count_zero_source_mask_choice_prime -> bpr_left_pc_count_zero_source_mask_choice_prime = 1 \/ bpr_right_pc_count_zero_source_mask_choice_prime = 1)) /\ pc_bit_count_zero_source_mask = 1) \/ (~((~(S (pc_index_count_zero_source_mask) = 1) /\ forall bpr_left_pc_count_zero_source_mask_choice_prime bpr_right_pc_count_zero_source_mask_choice_prime. S (pc_index_count_zero_source_mask) = bpr_left_pc_count_zero_source_mask_choice_prime * bpr_right_pc_count_zero_source_mask_choice_prime -> bpr_left_pc_count_zero_source_mask_choice_prime = 1 \/ bpr_right_pc_count_zero_source_mask_choice_prime = 1)) /\ pc_bit_count_zero_source_mask = 0)))) /\ (exists fs_u_pc_count_zero_source_sum fs_v_pc_count_zero_source_sum. ((((exists fs_h_pc_count_zero_source_sum_body_start. fs_h_pc_count_zero_source_sum_body_start + S (0) = S ((S (0)) * fs_v_pc_count_zero_source_sum)) /\ exists fs_q_pc_count_zero_source_sum_body_start. fs_u_pc_count_zero_source_sum = fs_q_pc_count_zero_source_sum_body_start * S ((S (0)) * fs_v_pc_count_zero_source_sum) + (0))) /\ ((((exists fs_h_pc_count_zero_source_sum_body_terminal. fs_h_pc_count_zero_source_sum_body_terminal + S (k) = S ((S (0)) * fs_v_pc_count_zero_source_sum)) /\ exists fs_q_pc_count_zero_source_sum_body_terminal. fs_u_pc_count_zero_source_sum = fs_q_pc_count_zero_source_sum_body_terminal * S ((S (0)) * fs_v_pc_count_zero_source_sum) + (k))) /\ forall fs_i_pc_count_zero_source_sum_body_steps. (exists fs_lt_pc_count_zero_source_sum_body_steps_bound. fs_lt_pc_count_zero_source_sum_body_steps_bound + S fs_i_pc_count_zero_source_sum_body_steps = 0) -> exists fs_a_pc_count_zero_source_sum_body_steps fs_r_pc_count_zero_source_sum_body_steps fs_s_pc_count_zero_source_sum_body_steps. ((((exists fs_h_pc_count_zero_source_sum_body_steps_summand. fs_h_pc_count_zero_source_sum_body_steps_summand + S (fs_a_pc_count_zero_source_sum_body_steps) = S ((S (fs_i_pc_count_zero_source_sum_body_steps)) * pc_scale_count_zero_source)) /\ exists fs_q_pc_count_zero_source_sum_body_steps_summand. pc_code_count_zero_source = fs_q_pc_count_zero_source_sum_body_steps_summand * S ((S (fs_i_pc_count_zero_source_sum_body_steps)) * pc_scale_count_zero_source) + (fs_a_pc_count_zero_source_sum_body_steps))) /\ ((((exists fs_h_pc_count_zero_source_sum_body_steps_partial. fs_h_pc_count_zero_source_sum_body_steps_partial + S (fs_r_pc_count_zero_source_sum_body_steps) = S ((S (fs_i_pc_count_zero_source_sum_body_steps)) * fs_v_pc_count_zero_source_sum)) /\ exists fs_q_pc_count_zero_source_sum_body_steps_partial. fs_u_pc_count_zero_source_sum = fs_q_pc_count_zero_source_sum_body_steps_partial * S ((S (fs_i_pc_count_zero_source_sum_body_steps)) * fs_v_pc_count_zero_source_sum) + (fs_r_pc_count_zero_source_sum_body_steps))) /\ ((((exists fs_h_pc_count_zero_source_sum_body_steps_successor. fs_h_pc_count_zero_source_sum_body_steps_successor + S (fs_s_pc_count_zero_source_sum_body_steps) = S ((S (S fs_i_pc_count_zero_source_sum_body_steps)) * fs_v_pc_count_zero_source_sum)) /\ exists fs_q_pc_count_zero_source_sum_body_steps_successor. fs_u_pc_count_zero_source_sum = fs_q_pc_count_zero_source_sum_body_steps_successor * S ((S (S fs_i_pc_count_zero_source_sum_body_steps)) * fs_v_pc_count_zero_source_sum) + (fs_s_pc_count_zero_source_sum_body_steps))) /\ fs_s_pc_count_zero_source_sum_body_steps = fs_r_pc_count_zero_source_sum_body_steps + fs_a_pc_count_zero_source_sum_body_steps))))))) -> k = 0Constructive proof overview
Generated structural guide
The exact prime count at zero is zero.
The unchanged tactic script uses 1 declared prerequisite and contains 10 exact native proof lines.
Alpha v34 checked-use · first admitted v27 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
beta_sum_zero Stable theorem; checked-use authorizedDirect dependents
none
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.