Exact expanded first-order arithmetic statement
forall u v p. (exists jt_gap_widthbound. jt_gap_widthbound+S (p)=(u*v)) -> ~(v=0)Constructive proof overview
Generated structural guide
A genuine index below u*v forces the rectangle width to be positive.
The unchanged tactic script uses 2 declared prerequisites and contains 16 exact native proof lines.
Alpha v35 checked-use · first admitted v35 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
lt_not_le Alpha theorem; checked-use authorized zero_le Alpha 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 assumptionsL1–5
02Establish hprodL6–15
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply lt not le.
03Use earlier factsL16–16
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L16
apply zero_le