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 p n q m a b c d. p + b = a + n -> q + d = c + m -> (p + q) + (b + d) = (a + c) + (n + m)Constructive proof overview
Generated structural guide
Component addition represents the sum of integer pairs even when either input has a different noncanonical positive/negative encoding.
The unchanged tactic script uses 1 declared prerequisite and contains 17 exact native proof lines.
Alpha v34 checked-use · first admitted v27 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
add_shuffle_middle 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 assumptionsL1–10
02Calculate and transport equalitiesL11–11
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L11
trans (p + b) + (q + d)
03Use earlier factsL12–12
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L12
apply add_shuffle_middle