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.
Exact expanded first-order arithmetic statement
forall n. S n * n + 2 * S n = S (S n) * S nConstructive proof overview
Generated structural guide
Consecutive triangular coefficients advance by exactly twice the next index.
The unchanged tactic script uses 2 declared prerequisites and contains 13 exact native proof lines.
Alpha v34 checked-use · first admitted v29 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
mul_comm Stable theorem; checked-use authorized mul_add Stable theorem; checked-use authorizedDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
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.
01Fix variables and assumptionsL1–1
Work with arbitrary variables or the premises of the current implication.
- L1
intro n
02Calculate and transport equalitiesL2–4
03Use earlier factsL5–5
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L5
apply mul_comm
04Calculate and transport equalitiesL6–7
05Use earlier factsL8–8
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L8
apply mul_add
06Calculate and transport equalitiesL9–12
07Use earlier factsL13–13
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L13
apply mul_comm