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
∀ n. Le(n,0) → n = 0Every 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
1 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall n. n <= 0 -> n = 0Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
BT002U gcd_exists_up_to BT0034 gcd_balanced_bezout_exists_up_to BT003E factor_search_up_to BT003K prime_divisor_exists_up_to BT0097 lt_three_cases BT00JD eisenstein_initial_segment_bit_count_functional BT00PS bounded_prime_interval_search BT00Q5 bounded_power_valuation_search BT00TM choose_positive BT00VV primorial_le_four_pow_boundedDefinition-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.
Named ingredients (1)
01Fix variables and assumptionsL1–2
02Separate the logical casesL3–3
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L3
cases h