BT0007

mul_add

Stable · empty-context checked

Multiplication distributes over addition on the right.

Exact expanded PA statement

forall n m k. n * (m + k) = n * m + n * k

Structural proof guide

Multiplication distributes over addition on the right.

Direct prerequisites: add_assoc. The authored body proceeds by structural induction (1).

Proof neighborhood

Direct dependencies

BT0003 add_assoc

Direct dependents

BT0008 mul_assoc BT000B add_mul BT001L mul_le_mul_left BT001S positive_quotient_gap_impossible BT002I divides_linear_step BT0033 balanced_bezout_euclid_step BT0037 common_divisor_divides_balanced_result BT003Q mod_eq_trans BT003R mod_eq_add BT004F binary_crt BT00R0 ceil_div_six_shift BT00R4 square_six_shift_identity BT00RD mul_le_cancel_left_nonzero BT00RG double_triple_remainder_complement_budget BT00TT choose_weighted_vertical BT00TU central_binom_succ_recurrence BT00U0 four_power_central_recurrence_step BT00VL central_binom_recurrence_double_bundle BT00VP central_binom_odd_middle_le_four_pow BT00W5 pow_eleven_two_le_pow_two_seven_from_total BT00W7 linear_square_budget BT00W8 bertrand_scaled_budget_root_32 BT00W9 bertrand_scaled_budget_root_33 BT00WA bertrand_scaled_budget_root_34 BT00WB bertrand_scaled_budget_root_35 BT00WC bertrand_scaled_budget_root_36 BT00WD bertrand_scaled_budget_root_37 BT00WP bertrand_h_root_32_from_total BT00WQ bertrand_h_root_33_from_total BT00WS bertrand_h_root_35_from_total BT00WT bertrand_h_root_36_from_total BT00X2 bertrand_hj_six_block_iterate_from_total BT00XG division_double_quotient_bit BT011C scaled_remainder_lift BT0121 bertrand_cover_one_hundred_sixty_three_three_hundred_seventeen BT0122 bertrand_cover_three_hundred_seventeen_five_hundred_twenty_one BT0123 bertrand_cutoff_lt_final_prime

Formal native tactic body

Dependencies are hypotheses of this body receipt. The focused endpoint audits separately check the complete empty-context certificates.

  1. 0001intro n
  2. 0002intro m
  3. 0003induction k
  4. 0004simp
  5. 0005simp [IH, add_assoc]