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 a c x. (((a) = (c) + (x) \/ (c) = (a) + (x))) -> x = 0 -> a = cConstructive proof overview
Generated structural guide
A zero witnessed absolute difference forces equality of its source coordinates.
The unchanged tactic script uses 0 declared prerequisites and contains 15 exact native proof lines.
dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged
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.
01Fix variables and assumptionsL1–5
02Separate the logical casesL6–6
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L6
cases hdifference
03Calculate and transport equalitiesL7–8
04Use earlier factsL9–9
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L9
exact hdifference_left
05Calculate and transport equalitiesL10–13
06Use earlier factsL14–14
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L14
exact hdifference_right
07Calculate and transport equalitiesL15–15
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L15
simp