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_inversetable_domain pfa_factor_right_inversetable_domain. (p) = pfa_factor_left_inversetable_domain * pfa_factor_right_inversetable_domain -> pfa_factor_left_inversetable_domain = 1 \/ pfa_factor_right_inversetable_domain = 1) -> exists b c. (forall pft_index_inversetable_result. (exists pfa_gap_inversetable_resultprefix. pfa_gap_inversetable_resultprefix + S (pft_index_inversetable_result) = (p)) -> exists pft_value_inversetable_result. (((((exists ff_h_pft_inversetable_resultpointentry. ff_h_pft_inversetable_resultpointentry + S (pft_value_inversetable_result) = S ((S (pft_index_inversetable_result)) * c)) /\ exists ff_q_pft_inversetable_resultpointentry. b = ff_q_pft_inversetable_resultpointentry * S ((S (pft_index_inversetable_result)) * c) + (pft_value_inversetable_result))) /\ ((((exists pfa_gap_inversetable_resultpointvalueinput. pfa_gap_inversetable_resultpointvalueinput + S (pft_index_inversetable_result) = (p)) /\ (((exists pfa_gap_inversetable_resultpointvalueoutput. pfa_gap_inversetable_resultpointvalueoutput + S (pft_value_inversetable_result) = (p)) /\ ((((pft_index_inversetable_result) = 0 /\ (pft_value_inversetable_result) = 0) \/ (((~((pft_index_inversetable_result) = 0)) /\ ((((exists pfa_gap_inversetable_resultpointvaluenonzeromultiplicationleft. pfa_gap_inversetable_resultpointvaluenonzeromultiplicationleft + S (pft_index_inversetable_result) = (p)) /\ (((exists pfa_gap_inversetable_resultpointvaluenonzeromultiplicationright. pfa_gap_inversetable_resultpointvaluenonzeromultiplicationright + S (pft_value_inversetable_result) = (p)) /\ ((((exists pfa_gap_inversetable_resultpointvaluenonzeromultiplicationresultbound. pfa_gap_inversetable_resultpointvaluenonzeromultiplicationresultbound + S (1) = (p)) /\ ((exists pfa_offset_left_inversetable_resultpointvaluenonzeromultiplicationresultcongruence pfa_offset_right_inversetable_resultpointvaluenonzeromultiplicationresultcongruence. ((pft_index_inversetable_result) * (pft_value_inversetable_result)) + (p) * pfa_offset_left_inversetable_resultpointvaluenonzeromultiplicationresultcongruence = (1) + (p) * pfa_offset_right_inversetable_resultpointvaluenonzeromultiplicationresultcongruence))))))))))))))))))))))Constructive proof overview
Generated structural guide
Construct every entry of the finite inverse 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_inverse_prefix_choice (p) - 0004
specialize prime_field_inverse_prefix_choice (p) - 0005
apply prime_field_inverse_prefix_choice - 0006
intro i - 0007
intro hi - 0008
specialize prime_field_zero_extended_inverse_exists (p) - 0009
specialize prime_field_zero_extended_inverse_exists (i) - 0010
apply prime_field_zero_extended_inverse_exists - 0011
exact hp - 0012
exact hi