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 PA statement
forall a b c d. (a + b) + (c + d) = (a + c) + (b + d)Structural proof guide
Four additive contributions can be regrouped by swapping the middle pair.
Direct prerequisites: add_comm, add_permute_outer. The authored body proceeds by direct introduction and elimination.
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are hypotheses of the historical Alpha-v12 body receipt. The complete historical Alpha-v18 proof bundle independently checks every dependency; current Alpha v25 preserves that checked theorem use without changing 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.
Named ingredients (2)
01Fix variables and assumptionsL1–4
02Calculate and transport equalitiesL5–6
03Use earlier factsL7–7
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L7
apply add_comm
04Calculate and transport equalitiesL8–9
05Use earlier factsL10–10
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L10
apply add_permute_outer
06Calculate and transport equalitiesL11–11
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L11
congr
07Use earlier factsL12–12
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L12
apply add_comm
08Calculate and transport equalitiesL13–13
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L13
refl