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. 1 * n = nEvery purple notation token opens its conservative definition. Expanding the displayed statement recovers the exact first-order Peano-arithmetic formula checked by the unchanged kernel.
Definitions used by this theorem
In the theorem statement
0 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall n. 1 * n = nProof neighborhood
Direct theorem prerequisites
Direct theorem 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_oneDefinition-aware tactic body
Only local propositions introduced by have or suffices are compacted. Every changed line has an exact-AST conservative-expansion receipt; the kernel still receives the immutable original tactic script.
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.