Exact expanded PA statement
forall n m k. (n * m) * k = n * (m * k)Structural proof guide
Generated structural guide
Multiplication is associative.
Use the direct prerequisites mul_add as previously established PA formulas.
The proof proceeds by structural induction (1), certified simplification (2).
Referenced ingredients
Proof neighborhood
Direct dependencies
Direct 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_gapFormal native tactic body
Dependencies are introduced as named hypotheses before line 1. Linked names are exact direct references. This Stable checked-use theorem is independently kernel-checked when replayed.