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
exists z d. (((exists ff_h_be_initial. ff_h_be_initial + S (1) = S ((S (0)) * d)) /\ exists ff_q_be_initial. z = ff_q_be_initial * S ((S (0)) * d) + (1)))Constructive proof overview
Generated structural guide
There is a real beta code whose initial square-and-multiply accumulator is one.
The unchanged tactic script uses 1 declared prerequisite and contains 8 exact native proof lines.
Alpha v34 checked-use · first admitted v22 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
beta_at_self_of_bound 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.
01Construct an explicit witnessL1–2
02Use earlier factsL3–6
03Construct an explicit witnessL7–7
Supply the displayed value, then prove that it has the required property.
- L7
exists 0
04Calculate and transport equalitiesL8–8
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L8
simp