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_zero_domain pfa_factor_right_zero_domain. (p) = pfa_factor_left_zero_domain * pfa_factor_right_zero_domain -> pfa_factor_left_zero_domain = 1 \/ pfa_factor_right_zero_domain = 1) -> (exists pfa_gap_zero_bound. pfa_gap_zero_bound + S (0) = (p))Constructive proof overview
Generated structural guide
Zero is a canonical representative at every prime, including two.
The unchanged tactic script uses 2 declared prerequisites and contains 9 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
prime_nonzero Stable theorem; checked-use authorized one_le_of_ne_zero Stable theorem; checked-use authorizedDirect dependents
FP0007 prime_field_residue_modulus_zero FP0014 prime_field_add_zero_right FP0018 prime_field_multiply_zero_right FP001B prime_field_negate_exists FP002A prime_field_arithmetic_laws FP002D prime_field_zero_extended_inverse_exists FP0046 prime_field_inverse_table_zero FP004F prime_field_unit_trace_residueFormal 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 factsL3–4
03Fix variables and assumptionsL5–5
Work with arbitrary variables or the premises of the current implication.
- L5
intro hz