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 g a. ((((exists ec_gcd_left_egt_zero. a = g * ec_gcd_left_egt_zero) /\ (exists ec_gcd_right_egt_zero. 0 = g * ec_gcd_right_egt_zero)) /\ forall ec_gcd_common_egt_zero. (exists ec_gcd_common_left_egt_zero. a = ec_gcd_common_egt_zero * ec_gcd_common_left_egt_zero) -> (exists ec_gcd_common_right_egt_zero. 0 = ec_gcd_common_egt_zero * ec_gcd_common_right_egt_zero) -> exists ec_gcd_greatest_egt_zero. g = ec_gcd_common_egt_zero * ec_gcd_greatest_egt_zero)) -> g = aConstructive proof overview
Generated structural guide
Any relational gcd at a zero-remainder terminal state is exactly its nonzero-side dividend, including a=0.
The unchanged tactic script uses 2 declared prerequisites and contains 11 exact native proof lines.
Alpha v34 checked-use · first admitted v22 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
is_gcd_zero_right Stable theorem; checked-use authorized is_gcd_unique 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.