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 B C D s t. A = s + B -> C = t + D -> A * C + B * D = s * t + (A * D + B * C)Constructive proof overview
Generated structural guide
Two actual nonnegative signed gaps multiply with an exact, subtraction-free compensation identity.
The unchanged tactic script uses 5 declared prerequisites and contains 9 exact native proof lines.
Alpha v34 checked-use · first admitted v28 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
add_mul Stable theorem; checked-use authorized mul_add Stable theorem; checked-use authorized add_assoc Stable theorem; checked-use authorized add_comm Stable theorem; checked-use authorized four_square_add_swap_right_tail Alpha 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 assumptionsL1–8
02Calculate and transport equalitiesL9–9
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L9
simp [hA, hC, add_mul, mul_add, add_assoc, add_comm, four_square_add_swap_right_tail]