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. n * 1 = nStructural proof guide
Generated structural guide
One is a right identity for multiplication.
Use the direct prerequisites zero_add as previously established PA formulas.
The proof proceeds by certified simplification (1).
Referenced ingredients
Proof neighborhood
Direct dependencies
Direct 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_gapFormal 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.