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. 1 * n = nStructural proof guide
One is a left identity for multiplication.
Direct prerequisites: none. The authored body proceeds by structural induction (1).
Proof neighborhood
Direct dependencies
Direct dependents
BT0020 mul_eq_one_components BT0027 one_multiple BT0039 gauss_coprime_cancel BT0055 le_scaled_nonzero BT005E beta_prefix_product_trace_exists BT0089 beta_prefix_sum_trace_exists BT0093 pow_one_from_zero_successor BT00PX le_mul_of_one_le_left BT00U2 central_binom_four_weighted_of_recurrence BT00VM central_binom_strong_upper_of_laws BT00YF division_three_scaled_upper_of_quotient_lt BT011N prime_five_hundred_twenty_one BT0122 bertrand_cover_three_hundred_seventeen_five_hundred_twenty_oneFormal native tactic body
Dependencies are hypotheses of the historical Alpha-v12 body receipt. The complete historical Alpha-v18 proof bundle independently checks every dependency; current Alpha v25 preserves that checked theorem use without changing 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.