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 ap an bp bn cp cn dp dn ep en fp fn. (((((((((ap) + (cp))) + (ep))) + (((an) + (((cn) + (en)))))) = ((((ap) + (((cp) + (ep))))) + (((((an) + (cn))) + (en))))) /\ (((((((bp) + (dp))) + (fp))) + (((bn) + (((dn) + (fn)))))) = ((((bp) + (((dp) + (fp))))) + (((((bn) + (dn))) + (fn)))))))Constructive proof overview
Generated structural guide
Actual signed-coordinate Gaussian sums associate by proved natural addition identities.
The unchanged tactic script uses 1 declared prerequisite and contains 15 exact native proof lines.
Alpha v34 checked-use · first admitted v30 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
add_assoc 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.
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–12
03Separate the logical casesL13–13
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L13
split