Exact expanded first-order arithmetic statement
(((exists mv_even_half_zeroeven. (0) = 2 * mv_even_half_zeroeven) /\ ((2) = 2))) \/ (((exists mv_odd_half_zeroodd. (0) = 2 * mv_odd_half_zeroodd + 1) /\ ((2) = 1)))Constructive proof overview
Generated structural guide
Exponent zero has canonical positive-unit code two, not code one.
The unchanged tactic script uses 0 declared prerequisites and contains 6 exact native proof lines.
Public research checkpoint: original HA and independently compiled Lean verified; not Alpha-enrolled, no Alpha checked-use authority; 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. The literal dependency-closed bundle is checked by original HA and the independently compiled Lean verifier. Public delivery grants no Alpha checked-use authority or 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.
01Separate the logical casesL1–2
02Construct an explicit witnessL3–3
Supply the displayed value, then prove that it has the required property.
- L3
exists 0
03Calculate and transport equalitiesL4–4
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L4
symm
04Use earlier factsL5–5
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L5
apply PA5
05Calculate and transport equalitiesL6–6
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L6
refl