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. ~(S n = 0)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. ~(S n = 0)Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
BT0022 mul_left_cancel_nonzero BT003E factor_search_up_to BT003G prime_nonzero BT003Y beta_modulus_nonzero BT004M bounded_common_multiple_step BT004N bounded_common_multiple_exists BT005C bounded_beta_exclusive_recode_invariant BT005E beta_prefix_product_trace_exists BT0069 beta_factor_divides_product BT007U beta_repeat_empty BT0084 beta_range_empty BT0089 beta_prefix_sum_trace_exists BT00R1 ceil_div_six_total BT00R9 square_lt_successor_square BT00RG double_triple_remainder_complement_budget BT00RK factorial_nonzero BT00RP prime_factorial_valuation_succ BT00S0 prime_power_quotient_prefix_exists BT00SF eisenstein_initial_segment_prefix_exists BT00SH division_successor_quotient_by_bit BT00SK power_quotient_successor_pointwise_add BT00T3 beta_pascal_zero_row_exists BT00T5 beta_pascal_row_step_exists BT00T7 beta_pascal_table_prefix_exists BT00T9 beta_pascal_zero_row_pointwise_functional BT00TA beta_pascal_row_step_pointwise_functional BT00TB beta_pascal_table_row_pointwise_functional BT00TE choose_zero BT00TF beta_pascal_table_diagonal_boundary BT00TH beta_pascal_table_successor_cell_recurrence BT00U8 primorial_factor_prefix_exists BT00US primorial_interval_factor_prefix_exists BT00VB factorial_prime_le_of_divides BT00VK central_binom_strong_upper_step BT00WE ceil_div_six_budget_of_scaled_le BT00X1 six_block_window_decomposition_above_thirty_two BT00XX double_quotient_carry_prefix_exists BT00YQ prime_contribution_prefix_exists BT010L prime_contribution_interval_prefix_existsDefinition-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.
01Use earlier factsL1–1
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L1
apply PA1
Original defined command ledger · 1 lines
- 0001
apply PA1