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 m. S n = S m -> n = mStructural proof guide
Generated structural guide
Successor is injective (the reusable PA2 lemma).
This root lemma is proved directly from the PA rules and the hypotheses introduced by its statement.
The proof proceeds by direct introduction and elimination.
Referenced ingredients
Proof neighborhood
Direct dependencies
Direct dependents
PA007D beta_magnitude_predecessor_recode_exists PA008E prime_mul_index_map_injective PA009M beta_prefix_append_two_scaled_orbit_closed PA00AE finite_prefix_choose_unused_nonendpoint PA00AG prime_bounded_square_one_cases PA00AH prime_inverse_prefix_fixed_cases PA00AL bounded_inverse_index_unique PA00AQ prime_inverse_prefix_nonendpoint_mate PA00BJ prime_factorial_wilson_congruenceFormal native tactic body
Dependencies are introduced as named hypotheses before line 1. Linked names are exact direct references. This Stable checked-use theorem is independently kernel-checked when replayed.
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.
01Use earlier factsL1–1
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L1
apply PA2