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.
Statement with defined notation
forall n m. S n = S m -> n = mEvery purple notation token opens its conservative definition. This is a reading surface; the compiler expands the statement before the unchanged kernel checks it.
Definitions used by this theorem
In the theorem statement
0 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall n m. S n = S m -> n = mProof neighborhood
Direct theorem prerequisites
Direct theorem 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_congruenceDefinition-aware tactic body
Only local propositions introduced by have or suffices are compacted. The untrusted compiler re-expands each one before the original tactic script is replayed; defined notation is never accepted by the kernel. Open the exact replay line beneath every changed command.
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