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 + n * kEvery purple notation token opens its conservative definition. Expanding the displayed statement recovers the exact first-order Peano-arithmetic formula checked by the unchanged kernel.
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 + n * kProof neighborhood
Direct theorem prerequisites
Direct theorem 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_primeDefinition-aware tactic body
Only local propositions introduced by have or suffices are compacted. Every changed line has an exact-AST conservative-expansion receipt; the kernel still receives the immutable original tactic script.
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.