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
∀ s. Lt(2,s) → Le(3 · s,s · s)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
2 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall s. (exists bcf_le_gap_b5rbtmsts_source. bcf_le_gap_b5rbtmsts_source + (3) = s) -> (exists bcf_le_gap_b5rbtmsts_result. bcf_le_gap_b5rbtmsts_result + (3 * s) = s * s)Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-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
Original defined command ledger · 7 lines
- 0001
intro s - 0002
intro hthree - 0003
specialize mul_le_mul_right 3 - 0004
specialize mul_le_mul_right s - 0005
specialize mul_le_mul_right s - 0006
apply mul_le_mul_right - 0007
exact hthree