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 m k. (n * m) * k = n * (m * k)Every 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 m k. (n * m) * k = n * (m * k)Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
PA000C multiple_mul_right PA0014 divides_remainder PA0018 multiple_trans PA001G divides_linear_step PA001J balanced_bezout_euclid_step PA001N balanced_combination_scale_right PA001O common_divisor_divides_balanced_result PA001Y mod_eq_mul_right PA0026 binary_crt PA0027 mod_eq_of_mod_eq_multiple PA003Q coprime_mod_inverse PA003R mod_eq_cancel_coprime PA0052 beta_product_replace_balance PA005N square_decomp PA005X pow_add PA00AK bounded_mod_inverse_unique PA006C mul_double_right PA006R four_mul_eq_double_double PA006U even_mul_left PA007N beta_product_pointwise_mul_exact PA007Q beta_product_pointwise_scale_mod PA008N scaled_inverse_from_unit_inverse PA00A0 beta_adjacent_target_pairs_product_power PA00B9 beta_adjacent_unit_pairs_product_one 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.