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. S n + m = S (n + m)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. S n + m = S (n + m)Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
BT0002 add_comm BT000H drop_add_prefix_from_fixed BT000X le_succ_self BT0018 le_succ BT0019 lt_to_le BT001B lt_irrefl_expanded BT001C le_eq_or_lt BT001F lt_trans BT001K lt_not_eq_add_middle BT001O division_remainder_succ BT004J common_divisor_beta_moduli_divides_gap_times_c BT008P bit_count_bounded BT0092 factorial_succ_decompose BT00R0 ceil_div_six_shift BT00SW bertrand_h_six_step_transport_from_total BT00TL choose_symmetry BT00TM choose_positive BT00TS central_binom_succ_double_middle BT00TT choose_weighted_vertical BT00VA factorial_prime_divides_of_le BT00VH primorial_odd_interval_divides_middle BT00VJ primorial_odd_interval_le_middle BT00VK central_binom_strong_upper_step BT00VR double_half_predecessor_data BT00VS odd_positive_prefix_predecessor_bound BT00VV primorial_le_four_pow_bounded BT00XB add_lt_add 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.