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. 0 + n = nEvery 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. 0 + n = nProof neighborhood
Direct theorem prerequisites
Direct theorem dependents
BT0002 add_comm BT000A mul_one BT000E le_refl BT000H drop_add_prefix_from_fixed BT000X le_succ_self BT001C le_eq_or_lt BT001O division_remainder_succ BT001U division_remainder_unique BT002G factor_difference BT0034 gcd_balanced_bezout_exists_up_to BT0040 beta_at_self_of_bound BT0046 dvd_to_mod_zero BT004F binary_crt BT004J common_divisor_beta_moduli_divides_gap_times_c BT0092 factorial_succ_decompose BT00QH power_valuation_successor_not_divides BT00R1 ceil_div_six_total BT00RA floor_sqrt_total BT00SA prime_power_quotient_tail_zero BT00SS prime_power_quotient_prefix_last_zero BT00TL choose_symmetry BT00TT choose_weighted_vertical BT00VA factorial_prime_divides_of_le BT00VK central_binom_strong_upper_step BT00X0 floor_sqrt_factorized_threshold_thirty_two BT00XF division_zero_quotient_of_lt BT00XQ power_quotient_prefix_sum_extend_zero BT00YC double_quotient_carry_prefix_entries_zero BT0126 bertrand_upper_endpoint_factorizationDefinition-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.