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 k u v. u = v -> (exists pa_b_pvs_transport_source pa_c_pvs_transport_source. ((forall pa_i_pvs_transport_source_repeat. (exists pa_lt_pvs_transport_source_repeat_bound. pa_lt_pvs_transport_source_repeat_bound + S pa_i_pvs_transport_source_repeat = k) -> (((exists pa_h_pvs_transport_source_repeat_decoded. pa_h_pvs_transport_source_repeat_decoded + S (a) = S ((S (pa_i_pvs_transport_source_repeat)) * pa_c_pvs_transport_source)) /\ exists pa_q_pvs_transport_source_repeat_decoded. pa_b_pvs_transport_source = pa_q_pvs_transport_source_repeat_decoded * S ((S (pa_i_pvs_transport_source_repeat)) * pa_c_pvs_transport_source) + (a)))) /\ (exists pa_u_pvs_transport_source_product pa_v_pvs_transport_source_product. ((((exists pa_h_pvs_transport_source_product_start. pa_h_pvs_transport_source_product_start + S (1) = S ((S (0)) * pa_v_pvs_transport_source_product)) /\ exists pa_q_pvs_transport_source_product_start. pa_u_pvs_transport_source_product = pa_q_pvs_transport_source_product_start * S ((S (0)) * pa_v_pvs_transport_source_product) + (1))) /\ ((((exists pa_h_pvs_transport_source_product_terminal. pa_h_pvs_transport_source_product_terminal + S (u) = S ((S (k)) * pa_v_pvs_transport_source_product)) /\ exists pa_q_pvs_transport_source_product_terminal. pa_u_pvs_transport_source_product = pa_q_pvs_transport_source_product_terminal * S ((S (k)) * pa_v_pvs_transport_source_product) + (u))) /\ forall pa_i_pvs_transport_source_product. (exists pa_lt_pvs_transport_source_product_bound. pa_lt_pvs_transport_source_product_bound + S pa_i_pvs_transport_source_product = k) -> exists pa_p_pvs_transport_source_product pa_r_pvs_transport_source_product pa_s_pvs_transport_source_product. ((((exists pa_h_pvs_transport_source_product_factor. pa_h_pvs_transport_source_product_factor + S (pa_p_pvs_transport_source_product) = S ((S (pa_i_pvs_transport_source_product)) * pa_c_pvs_transport_source)) /\ exists pa_q_pvs_transport_source_product_factor. pa_b_pvs_transport_source = pa_q_pvs_transport_source_product_factor * S ((S (pa_i_pvs_transport_source_product)) * pa_c_pvs_transport_source) + (pa_p_pvs_transport_source_product))) /\ ((((exists pa_h_pvs_transport_source_product_partial. pa_h_pvs_transport_source_product_partial + S (pa_r_pvs_transport_source_product) = S ((S (pa_i_pvs_transport_source_product)) * pa_v_pvs_transport_source_product)) /\ exists pa_q_pvs_transport_source_product_partial. pa_u_pvs_transport_source_product = pa_q_pvs_transport_source_product_partial * S ((S (pa_i_pvs_transport_source_product)) * pa_v_pvs_transport_source_product) + (pa_r_pvs_transport_source_product))) /\ ((((exists pa_h_pvs_transport_source_product_successor. pa_h_pvs_transport_source_product_successor + S (pa_s_pvs_transport_source_product) = S ((S (S pa_i_pvs_transport_source_product)) * pa_v_pvs_transport_source_product)) /\ exists pa_q_pvs_transport_source_product_successor. pa_u_pvs_transport_source_product = pa_q_pvs_transport_source_product_successor * S ((S (S pa_i_pvs_transport_source_product)) * pa_v_pvs_transport_source_product) + (pa_s_pvs_transport_source_product))) /\ pa_s_pvs_transport_source_product = pa_r_pvs_transport_source_product * pa_p_pvs_transport_source_product)))))))) -> (exists pa_b_pvs_transport_target pa_c_pvs_transport_target. ((forall pa_i_pvs_transport_target_repeat. (exists pa_lt_pvs_transport_target_repeat_bound. pa_lt_pvs_transport_target_repeat_bound + S pa_i_pvs_transport_target_repeat = k) -> (((exists pa_h_pvs_transport_target_repeat_decoded. pa_h_pvs_transport_target_repeat_decoded + S (a) = S ((S (pa_i_pvs_transport_target_repeat)) * pa_c_pvs_transport_target)) /\ exists pa_q_pvs_transport_target_repeat_decoded. pa_b_pvs_transport_target = pa_q_pvs_transport_target_repeat_decoded * S ((S (pa_i_pvs_transport_target_repeat)) * pa_c_pvs_transport_target) + (a)))) /\ (exists pa_u_pvs_transport_target_product pa_v_pvs_transport_target_product. ((((exists pa_h_pvs_transport_target_product_start. pa_h_pvs_transport_target_product_start + S (1) = S ((S (0)) * pa_v_pvs_transport_target_product)) /\ exists pa_q_pvs_transport_target_product_start. pa_u_pvs_transport_target_product = pa_q_pvs_transport_target_product_start * S ((S (0)) * pa_v_pvs_transport_target_product) + (1))) /\ ((((exists pa_h_pvs_transport_target_product_terminal. pa_h_pvs_transport_target_product_terminal + S (v) = S ((S (k)) * pa_v_pvs_transport_target_product)) /\ exists pa_q_pvs_transport_target_product_terminal. pa_u_pvs_transport_target_product = pa_q_pvs_transport_target_product_terminal * S ((S (k)) * pa_v_pvs_transport_target_product) + (v))) /\ forall pa_i_pvs_transport_target_product. (exists pa_lt_pvs_transport_target_product_bound. pa_lt_pvs_transport_target_product_bound + S pa_i_pvs_transport_target_product = k) -> exists pa_p_pvs_transport_target_product pa_r_pvs_transport_target_product pa_s_pvs_transport_target_product. ((((exists pa_h_pvs_transport_target_product_factor. pa_h_pvs_transport_target_product_factor + S (pa_p_pvs_transport_target_product) = S ((S (pa_i_pvs_transport_target_product)) * pa_c_pvs_transport_target)) /\ exists pa_q_pvs_transport_target_product_factor. pa_b_pvs_transport_target = pa_q_pvs_transport_target_product_factor * S ((S (pa_i_pvs_transport_target_product)) * pa_c_pvs_transport_target) + (pa_p_pvs_transport_target_product))) /\ ((((exists pa_h_pvs_transport_target_product_partial. pa_h_pvs_transport_target_product_partial + S (pa_r_pvs_transport_target_product) = S ((S (pa_i_pvs_transport_target_product)) * pa_v_pvs_transport_target_product)) /\ exists pa_q_pvs_transport_target_product_partial. pa_u_pvs_transport_target_product = pa_q_pvs_transport_target_product_partial * S ((S (pa_i_pvs_transport_target_product)) * pa_v_pvs_transport_target_product) + (pa_r_pvs_transport_target_product))) /\ ((((exists pa_h_pvs_transport_target_product_successor. pa_h_pvs_transport_target_product_successor + S (pa_s_pvs_transport_target_product) = S ((S (S pa_i_pvs_transport_target_product)) * pa_v_pvs_transport_target_product)) /\ exists pa_q_pvs_transport_target_product_successor. pa_u_pvs_transport_target_product = pa_q_pvs_transport_target_product_successor * S ((S (S pa_i_pvs_transport_target_product)) * pa_v_pvs_transport_target_product) + (pa_s_pvs_transport_target_product))) /\ pa_s_pvs_transport_target_product = pa_r_pvs_transport_target_product * pa_p_pvs_transport_target_product))))))))Constructive proof overview
Generated structural guide
Transport the actual terminal value of a power trace along equality.
The unchanged tactic script uses 0 declared prerequisites and contains 9 exact native proof lines.
Alpha v34 checked-use · first admitted v29 · 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.
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 assumptionsL1–6
02Calculate and transport equalitiesL7–8
03Use earlier factsL9–9
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L9
exact hpow