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 PA statement
forall n z. (((exists bcf_lt_gap_bcbp_source_out_of_range. bcf_lt_gap_bcbp_source_out_of_range + S (n + n) = n) /\ z = 0) \/ ((exists bcf_le_gap_bcbp_source_in_range. bcf_le_gap_bcbp_source_in_range + (n) = n + n) /\ (exists bcf_row_code_code_bcbp_source bcf_row_code_scale_bcbp_source bcf_row_scale_code_bcbp_source bcf_row_scale_scale_bcbp_source bcf_row_code_bcbp_source bcf_row_scale_bcbp_source. ((forall bcf_row_index_bcbp_source_table. (exists bcf_lt_gap_bcbp_source_table_row_bound. bcf_lt_gap_bcbp_source_table_row_bound + S (bcf_row_index_bcbp_source_table) = S (n + n)) -> exists bcf_row_code_bcbp_source_table bcf_row_scale_bcbp_source_table. ((((exists bcf_height_bcbp_source_table_decoded_row_code. bcf_height_bcbp_source_table_decoded_row_code + S (bcf_row_code_bcbp_source_table) = S ((S (bcf_row_index_bcbp_source_table)) * bcf_row_code_scale_bcbp_source)) /\ exists bcf_quotient_bcbp_source_table_decoded_row_code. bcf_row_code_code_bcbp_source = bcf_quotient_bcbp_source_table_decoded_row_code * S ((S (bcf_row_index_bcbp_source_table)) * bcf_row_code_scale_bcbp_source) + (bcf_row_code_bcbp_source_table))) /\ ((((exists bcf_height_bcbp_source_table_decoded_row_scale. bcf_height_bcbp_source_table_decoded_row_scale + S (bcf_row_scale_bcbp_source_table) = S ((S (bcf_row_index_bcbp_source_table)) * bcf_row_scale_scale_bcbp_source)) /\ exists bcf_quotient_bcbp_source_table_decoded_row_scale. bcf_row_scale_code_bcbp_source = bcf_quotient_bcbp_source_table_decoded_row_scale * S ((S (bcf_row_index_bcbp_source_table)) * bcf_row_scale_scale_bcbp_source) + (bcf_row_scale_bcbp_source_table))) /\ ((bcf_row_index_bcbp_source_table = 0 /\ (forall bcf_index_bcbp_source_table_zero_row. (exists bcf_lt_gap_bcbp_source_table_zero_row_bound. bcf_lt_gap_bcbp_source_table_zero_row_bound + S (bcf_index_bcbp_source_table_zero_row) = S (n + n)) -> exists bcf_value_bcbp_source_table_zero_row. ((((exists bcf_height_bcbp_source_table_zero_row_entry. bcf_height_bcbp_source_table_zero_row_entry + S (bcf_value_bcbp_source_table_zero_row) = S ((S (bcf_index_bcbp_source_table_zero_row)) * bcf_row_scale_bcbp_source_table)) /\ exists bcf_quotient_bcbp_source_table_zero_row_entry. bcf_row_code_bcbp_source_table = bcf_quotient_bcbp_source_table_zero_row_entry * S ((S (bcf_index_bcbp_source_table_zero_row)) * bcf_row_scale_bcbp_source_table) + (bcf_value_bcbp_source_table_zero_row))) /\ ((bcf_index_bcbp_source_table_zero_row = 0 /\ bcf_value_bcbp_source_table_zero_row = 1) \/ exists bcf_predecessor_bcbp_source_table_zero_row. bcf_index_bcbp_source_table_zero_row = S bcf_predecessor_bcbp_source_table_zero_row /\ bcf_value_bcbp_source_table_zero_row = 0)))) \/ exists bcf_predecessor_bcbp_source_table bcf_previous_code_bcbp_source_table bcf_previous_scale_bcbp_source_table. bcf_row_index_bcbp_source_table = S bcf_predecessor_bcbp_source_table /\ ((((exists bcf_height_bcbp_source_table_decoded_previous_code. bcf_height_bcbp_source_table_decoded_previous_code + S (bcf_previous_code_bcbp_source_table) = S ((S (bcf_predecessor_bcbp_source_table)) * bcf_row_code_scale_bcbp_source)) /\ exists bcf_quotient_bcbp_source_table_decoded_previous_code. bcf_row_code_code_bcbp_source = bcf_quotient_bcbp_source_table_decoded_previous_code * S ((S (bcf_predecessor_bcbp_source_table)) * bcf_row_code_scale_bcbp_source) + (bcf_previous_code_bcbp_source_table))) /\ ((((exists bcf_height_bcbp_source_table_decoded_previous_scale. bcf_height_bcbp_source_table_decoded_previous_scale + S (bcf_previous_scale_bcbp_source_table) = S ((S (bcf_predecessor_bcbp_source_table)) * bcf_row_scale_scale_bcbp_source)) /\ exists bcf_quotient_bcbp_source_table_decoded_previous_scale. bcf_row_scale_code_bcbp_source = bcf_quotient_bcbp_source_table_decoded_previous_scale * S ((S (bcf_predecessor_bcbp_source_table)) * bcf_row_scale_scale_bcbp_source) + (bcf_previous_scale_bcbp_source_table))) /\ (forall bcf_index_bcbp_source_table_row_step. (exists bcf_lt_gap_bcbp_source_table_row_step_bound. bcf_lt_gap_bcbp_source_table_row_step_bound + S (bcf_index_bcbp_source_table_row_step) = S (n + n)) -> exists bcf_value_bcbp_source_table_row_step. ((((exists bcf_height_bcbp_source_table_row_step_entry. bcf_height_bcbp_source_table_row_step_entry + S (bcf_value_bcbp_source_table_row_step) = S ((S (bcf_index_bcbp_source_table_row_step)) * bcf_row_scale_bcbp_source_table)) /\ exists bcf_quotient_bcbp_source_table_row_step_entry. bcf_row_code_bcbp_source_table = bcf_quotient_bcbp_source_table_row_step_entry * S ((S (bcf_index_bcbp_source_table_row_step)) * bcf_row_scale_bcbp_source_table) + (bcf_value_bcbp_source_table_row_step))) /\ ((bcf_index_bcbp_source_table_row_step = 0 /\ bcf_value_bcbp_source_table_row_step = 1) \/ exists bcf_predecessor_bcbp_source_table_row_step bcf_left_bcbp_source_table_row_step bcf_right_bcbp_source_table_row_step. bcf_index_bcbp_source_table_row_step = S bcf_predecessor_bcbp_source_table_row_step /\ ((((exists bcf_height_bcbp_source_table_row_step_previous_left. bcf_height_bcbp_source_table_row_step_previous_left + S (bcf_left_bcbp_source_table_row_step) = S ((S (bcf_predecessor_bcbp_source_table_row_step)) * bcf_previous_scale_bcbp_source_table)) /\ exists bcf_quotient_bcbp_source_table_row_step_previous_left. bcf_previous_code_bcbp_source_table = bcf_quotient_bcbp_source_table_row_step_previous_left * S ((S (bcf_predecessor_bcbp_source_table_row_step)) * bcf_previous_scale_bcbp_source_table) + (bcf_left_bcbp_source_table_row_step))) /\ ((((exists bcf_height_bcbp_source_table_row_step_previous_right. bcf_height_bcbp_source_table_row_step_previous_right + S (bcf_right_bcbp_source_table_row_step) = S ((S (S (bcf_predecessor_bcbp_source_table_row_step))) * bcf_previous_scale_bcbp_source_table)) /\ exists bcf_quotient_bcbp_source_table_row_step_previous_right. bcf_previous_code_bcbp_source_table = bcf_quotient_bcbp_source_table_row_step_previous_right * S ((S (S (bcf_predecessor_bcbp_source_table_row_step))) * bcf_previous_scale_bcbp_source_table) + (bcf_right_bcbp_source_table_row_step))) /\ bcf_value_bcbp_source_table_row_step = bcf_left_bcbp_source_table_row_step + bcf_right_bcbp_source_table_row_step))))))))))) /\ ((((exists bcf_height_bcbp_source_decoded_row_code. bcf_height_bcbp_source_decoded_row_code + S (bcf_row_code_bcbp_source) = S ((S (n + n)) * bcf_row_code_scale_bcbp_source)) /\ exists bcf_quotient_bcbp_source_decoded_row_code. bcf_row_code_code_bcbp_source = bcf_quotient_bcbp_source_decoded_row_code * S ((S (n + n)) * bcf_row_code_scale_bcbp_source) + (bcf_row_code_bcbp_source))) /\ ((((exists bcf_height_bcbp_source_decoded_row_scale. bcf_height_bcbp_source_decoded_row_scale + S (bcf_row_scale_bcbp_source) = S ((S (n + n)) * bcf_row_scale_scale_bcbp_source)) /\ exists bcf_quotient_bcbp_source_decoded_row_scale. bcf_row_scale_code_bcbp_source = bcf_quotient_bcbp_source_decoded_row_scale * S ((S (n + n)) * bcf_row_scale_scale_bcbp_source) + (bcf_row_scale_bcbp_source))) /\ (((exists bcf_height_bcbp_source_decoded_value. bcf_height_bcbp_source_decoded_value + S (z) = S ((S (n)) * bcf_row_scale_bcbp_source)) /\ exists bcf_quotient_bcbp_source_decoded_value. bcf_row_code_bcbp_source = bcf_quotient_bcbp_source_decoded_value * S ((S (n)) * bcf_row_scale_bcbp_source) + (z))))))))) -> exists p. z = S pStructural proof guide
Every relational central-binomial value is a successor.
Direct prerequisites: choose_positive. The authored body proceeds by direct introduction and elimination.
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are hypotheses of the historical Alpha-v12 body receipt. The complete historical Alpha-v18 proof bundle independently checks every dependency; current Alpha v25 preserves that checked theorem use without changing 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.
Named ingredients (1)
01Fix variables and assumptionsL1–3
02Use earlier factsL4–7
03Construct an explicit witnessL8–8
Supply the displayed value, then prove that it has the required property.
- L8
exists n
04Calculate and transport equalitiesL9–9
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L9
refl
05Use earlier factsL10–10
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L10
exact hcentral
Original exact command ledger · 10 lines
- 0001
intro n - 0002
intro z - 0003
intro hcentral - 0004
specialize choose_positive (n + n) - 0005
specialize choose_positive n - 0006
specialize choose_positive z - 0007
apply choose_positive - 0008
exists n - 0009
refl - 0010
exact hcentral