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 m x r y s. (exists ff_left_binary_multiply_left ff_right_binary_multiply_left. (x) + m * ff_left_binary_multiply_left = (r) + m * ff_right_binary_multiply_left) -> (exists ff_left_binary_multiply_right ff_right_binary_multiply_right. (y) + m * ff_left_binary_multiply_right = (s) + m * ff_right_binary_multiply_right) -> (exists ff_left_binary_multiply_result ff_right_binary_multiply_result. (x * y) + m * ff_left_binary_multiply_result = (r * s) + m * ff_right_binary_multiply_result)Constructive proof overview
Generated structural guide
Multiplication preserves both witnessed modular factors.
The unchanged tactic script uses 1 declared prerequisite and contains 15 exact native proof lines.
Alpha v34 checked-use · first admitted v21 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
mod_eq_mul 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.