Exact expanded PA statement
forall n m k. (n * m) * k = n * (m * k)Structural proof guide
Multiplication is associative.
Direct prerequisites: mul_add. The authored body proceeds by structural induction (1).
Proof neighborhood
Direct dependencies
Direct dependents
BT002A multiple_mul_right BT002C multiple_trans BT002F multiple_antisymm BT002H divides_remainder BT002I divides_linear_step BT0033 balanced_bezout_euclid_step BT0036 balanced_combination_scale_right BT0037 common_divisor_divides_balanced_result BT003S mod_eq_mul_right BT004F binary_crt BT004T mod_eq_of_mod_eq_multiple BT009X pow_add BT00BG coprime_product_is_lcm BT00QJ mul_shuffle_four BT00QK power_divides_exponent_antitone BT00QM power_divides_successor_of_cofactor BT00QN prime_power_successor_cancel_cofactor BT00QV pow_mul_base BT00RG double_triple_remainder_complement_budget BT00TU central_binom_succ_recurrence BT00TW factorial_weighted_product_combine BT00U0 four_power_central_recurrence_step BT00U3 four_pow_central_seed_package BT00UQ beta_product_prefix_suffix_split BT00VK central_binom_strong_upper_step BT00VL central_binom_recurrence_double_bundle BT00VP central_binom_odd_middle_le_four_pow BT00W7 linear_square_budget BT00WC bertrand_scaled_budget_root_36 BT00WD bertrand_scaled_budget_root_37 BT00WO pow_thirty_six_double_block_eq_pow_six_four_block_from_total BT00WP bertrand_h_root_32_from_total BT00WR bertrand_h_root_34_from_total BT00WS bertrand_h_root_35_from_total BT00WT bertrand_h_root_36_from_total BT00WU bertrand_h_root_37_from_total BT00WX scaled_factor_square_identity BT0101 prime_contribution_selected_successor_divides BT0115 bertrand_eventually_closed_upper BT011C scaled_remainder_lift BT011N prime_five_hundred_twenty_one BT0122 bertrand_cover_three_hundred_seventeen_five_hundred_twenty_one BT0123 bertrand_cutoff_lt_final_primeFormal native tactic body
Dependencies are hypotheses of this body receipt. The focused endpoint audits separately check the complete empty-context certificates.