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 expanded first-order arithmetic statement
forall p. (~((p) = 1) /\ forall pfa_factor_left_addtable_domain pfa_factor_right_addtable_domain. (p) = pfa_factor_left_addtable_domain * pfa_factor_right_addtable_domain -> pfa_factor_left_addtable_domain = 1 \/ pfa_factor_right_addtable_domain = 1) -> exists b c. (forall pft_index_addtable_result. (exists pfa_gap_addtable_resultprefix. pfa_gap_addtable_resultprefix + S (pft_index_addtable_result) = ((p) * (p))) -> exists pft_value_addtable_result. (((((exists ff_h_pft_addtable_resultpointentry. ff_h_pft_addtable_resultpointentry + S (pft_value_addtable_result) = S ((S (pft_index_addtable_result)) * c)) /\ exists ff_q_pft_addtable_resultpointentry. b = ff_q_pft_addtable_resultpointentry * S ((S (pft_index_addtable_result)) * c) + (pft_value_addtable_result))) /\ ((exists pft_row_addtable_resultpointvalue pft_column_addtable_resultpointvalue. (((pft_index_addtable_result) = pft_row_addtable_resultpointvalue * (p) + pft_column_addtable_resultpointvalue) /\ ((((exists pfa_gap_addtable_resultpointvalueoperationleft. pfa_gap_addtable_resultpointvalueoperationleft + S (pft_row_addtable_resultpointvalue) = (p)) /\ (((exists pfa_gap_addtable_resultpointvalueoperationright. pfa_gap_addtable_resultpointvalueoperationright + S (pft_column_addtable_resultpointvalue) = (p)) /\ ((((exists pfa_gap_addtable_resultpointvalueoperationresultbound. pfa_gap_addtable_resultpointvalueoperationresultbound + S (pft_value_addtable_result) = (p)) /\ ((exists pfa_offset_left_addtable_resultpointvalueoperationresultcongruence pfa_offset_right_addtable_resultpointvalueoperationresultcongruence. ((pft_row_addtable_resultpointvalue) + (pft_column_addtable_resultpointvalue)) + (p) * pfa_offset_left_addtable_resultpointvalueoperationresultcongruence = (pft_value_addtable_result) + (p) * pfa_offset_right_addtable_resultpointvalueoperationresultcongruence))))))))))))))))Constructive proof overview
Generated structural guide
Construct every entry of the finite add table from primality alone.
The unchanged tactic script uses 2 declared prerequisites and contains 12 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
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.
Named ingredients (2)
01Fix variables and assumptionsL1–2
02Use earlier factsL3–5
03Fix variables and assumptionsL6–7
Original exact command ledger · 12 lines
- 0001
intro p - 0002
intro hp - 0003
specialize prime_field_add_prefix_choice (p) - 0004
specialize prime_field_add_prefix_choice ((p) * (p)) - 0005
apply prime_field_add_prefix_choice - 0006
intro i - 0007
intro hi - 0008
specialize prime_field_add_grid_value_exists (p) - 0009
specialize prime_field_add_grid_value_exists (i) - 0010
apply prime_field_add_grid_value_exists - 0011
exact hp - 0012
exact hi