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. n * 1 = nEvery 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. n * 1 = nProof neighborhood
Direct theorem prerequisites
Direct theorem dependents
PA0003 prime_divisor_eq_one_or_self PA0019 multiple_refl PA0026 binary_crt PA003R mod_eq_cancel_coprime PA005D predecessor_square_mod_one PA005X pow_add PA00AK bounded_mod_inverse_unique PA0070 gauss_pointwise_signed_half_representative PA007I beta_sign_factor_product_power PA007P gauss_signed_pointwise_mul_scale_mod PA008L fermat_predecessor_exponent_mod_one PA008N scaled_inverse_from_unit_inverse PA00A3 factorial_one_value PA00C4 predecessor_multiple_mod_complement PA00DQ odd_half_cross_product_gapDefinition-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.