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. 0 * n = 0Every 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. 0 * n = 0Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
PA000H mul_comm PA000N mul_eq_one_components PA0031 prime_nonzero PA0034 beta_half_range_entry_bounds PA003E beta_at_self_of_bound PA006Y odd_upper_remainder_reflection PA007C gauss_signed_half_magnitude_injective PA00A2 prime_two_or_terminal_odd_shape PA00C2 odd_half_strictly_below_modulus PA00EK beta_repeat_sum_exact PA00ES eisenstein_zero_width_rectangle_sum_zeroDefinition-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.