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 k a b. (exists ftcn_left_fssq_zero_swap_source ftcn_right_fssq_zero_swap_source. (a + b) + (k) * ftcn_left_fssq_zero_swap_source = (0) + (k) * ftcn_right_fssq_zero_swap_source) -> (exists ftcn_left_fssq_zero_swap_result ftcn_right_fssq_zero_swap_result. (b + a) + (k) * ftcn_left_fssq_zero_swap_result = (0) + (k) * ftcn_right_fssq_zero_swap_result)Constructive proof overview
Generated structural guide
Swapping the two summands of a modular zero balance preserves that balance.
The unchanged tactic script uses 1 declared prerequisite and contains 8 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
Historical empty-context replay experiment only; that experiment persisted no certificate and granted no release authority. Current checked use follows separately sealed, independently verified proof bundles; there is no Stable promotion.
Proof neighborhood
Direct dependencies
add_comm 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.