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. 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. 1 * n = nProof neighborhood
Direct theorem prerequisites
Direct theorem dependents
PA000N mul_eq_one_components PA001P gauss_coprime_cancel PA002N le_scaled_nonzero PA003G beta_prefix_sum_trace_exists PA003W beta_prefix_product_trace_exists PA005E pow_predecessor_parity_mod PA005T pow_one_from_zero_successor PA00AK bounded_mod_inverse_unique PA007N beta_product_pointwise_mul_exact PA007Q beta_product_pointwise_scale_mod PA00AO inverse_prefix_zero_fixed PA00B9 beta_adjacent_unit_pairs_product_one PA00BI mod_one_product_restore_predecessor 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.