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. (exists pa_b_bl_zero_power pa_c_bl_zero_power. ((forall pa_i_bl_zero_power_repeat. (exists pa_lt_bl_zero_power_repeat_bound. pa_lt_bl_zero_power_repeat_bound + S pa_i_bl_zero_power_repeat = 0) -> (((exists pa_h_bl_zero_power_repeat_decoded. pa_h_bl_zero_power_repeat_decoded + S (2) = S ((S (pa_i_bl_zero_power_repeat)) * pa_c_bl_zero_power)) /\ exists pa_q_bl_zero_power_repeat_decoded. pa_b_bl_zero_power = pa_q_bl_zero_power_repeat_decoded * S ((S (pa_i_bl_zero_power_repeat)) * pa_c_bl_zero_power) + (2)))) /\ (exists pa_u_bl_zero_power_product pa_v_bl_zero_power_product. ((((exists pa_h_bl_zero_power_product_start. pa_h_bl_zero_power_product_start + S (1) = S ((S (0)) * pa_v_bl_zero_power_product)) /\ exists pa_q_bl_zero_power_product_start. pa_u_bl_zero_power_product = pa_q_bl_zero_power_product_start * S ((S (0)) * pa_v_bl_zero_power_product) + (1))) /\ ((((exists pa_h_bl_zero_power_product_terminal. pa_h_bl_zero_power_product_terminal + S (p) = S ((S (0)) * pa_v_bl_zero_power_product)) /\ exists pa_q_bl_zero_power_product_terminal. pa_u_bl_zero_power_product = pa_q_bl_zero_power_product_terminal * S ((S (0)) * pa_v_bl_zero_power_product) + (p))) /\ forall pa_i_bl_zero_power_product. (exists pa_lt_bl_zero_power_product_bound. pa_lt_bl_zero_power_product_bound + S pa_i_bl_zero_power_product = 0) -> exists pa_p_bl_zero_power_product pa_r_bl_zero_power_product pa_s_bl_zero_power_product. ((((exists pa_h_bl_zero_power_product_factor. pa_h_bl_zero_power_product_factor + S (pa_p_bl_zero_power_product) = S ((S (pa_i_bl_zero_power_product)) * pa_c_bl_zero_power)) /\ exists pa_q_bl_zero_power_product_factor. pa_b_bl_zero_power = pa_q_bl_zero_power_product_factor * S ((S (pa_i_bl_zero_power_product)) * pa_c_bl_zero_power) + (pa_p_bl_zero_power_product))) /\ ((((exists pa_h_bl_zero_power_product_partial. pa_h_bl_zero_power_product_partial + S (pa_r_bl_zero_power_product) = S ((S (pa_i_bl_zero_power_product)) * pa_v_bl_zero_power_product)) /\ exists pa_q_bl_zero_power_product_partial. pa_u_bl_zero_power_product = pa_q_bl_zero_power_product_partial * S ((S (pa_i_bl_zero_power_product)) * pa_v_bl_zero_power_product) + (pa_r_bl_zero_power_product))) /\ ((((exists pa_h_bl_zero_power_product_successor. pa_h_bl_zero_power_product_successor + S (pa_s_bl_zero_power_product) = S ((S (S pa_i_bl_zero_power_product)) * pa_v_bl_zero_power_product)) /\ exists pa_q_bl_zero_power_product_successor. pa_u_bl_zero_power_product = pa_q_bl_zero_power_product_successor * S ((S (S pa_i_bl_zero_power_product)) * pa_v_bl_zero_power_product) + (pa_s_bl_zero_power_product))) /\ pa_s_bl_zero_power_product = pa_r_bl_zero_power_product * pa_p_bl_zero_power_product)))))))) -> p = 1Constructive proof overview
Generated structural guide
The beta-coded zeroth power of two is exactly one.
The unchanged tactic script uses 1 declared prerequisite and contains 8 exact native proof lines.
Alpha v34 checked-use · first admitted v22 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
pow_zero 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 assumptionsL1–2
02Use earlier factsL3–6
03Calculate and transport equalitiesL7–7
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L7
refl
04Use earlier factsL8–8
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L8
exact hp