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. 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 + k)Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
BT0005 mul_succ_left BT0007 mul_add BT000F le_trans BT000I antisymm_from_witnesses BT0014 add_le_add_right BT0015 add_le_add_left BT001E lt_of_le_of_lt BT001F lt_trans BT001R division_block_upper BT001S positive_quotient_gap_impossible BT002G factor_difference BT0032 add_permute_outer BT0033 balanced_bezout_euclid_step BT003Q mod_eq_trans BT004C bezout_mod_left BT004D bezout_mod_right BT004E mod_eq_predecessor_cancel BT008P bit_count_bounded BT00K5 beta_sum_pointwise_add BT00R0 ceil_div_six_shift BT00R4 square_six_shift_identity BT00RG double_triple_remainder_complement_budget BT00SW bertrand_h_six_step_transport_from_total BT00SX bertrand_j_six_step_transport_from_total BT00TT choose_weighted_vertical BT00VK central_binom_strong_upper_step BT00W4 pow_three_five_le_pow_four_four_from_total 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 BT00WT bertrand_h_root_36_from_total BT00X1 six_block_window_decomposition_above_thirty_two BT00X2 bertrand_hj_six_block_iterate_from_total BT00XC add_lt_cancel_left BT00XG division_double_quotient_bit BT00Y2 division_successor_quotient_divisor_le BT00Y3 beta_sum_double_carry_exact BT011C scaled_remainder_lift BT011K prime_eighty_three BT011L prime_one_hundred_sixty_three BT011M prime_three_hundred_seventeen BT011N prime_five_hundred_twenty_one BT011O bertrand_add_swap_nested BT011P bertrand_add_six_permute BT0120 bertrand_cover_eighty_three_one_hundred_sixty_three 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.
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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.