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 q i. (exists mdr_gap_square_index. mdr_gap_square_index + S (i) = (q * q)) -> ~(q = 0)Constructive proof overview
Generated structural guide
An actual index in a square prefix proves its row width is nonzero; zero-dimensional bounds remain genuinely vacuous.
The unchanged tactic script uses 1 declared prerequisite and contains 12 exact native proof lines.
Alpha v34 checked-use · first admitted v27 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
Direct 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.
Named ingredients (1)
01Fix variables and assumptionsL1–4
02Establish hlengthL5–12
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply PA5.