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 n m. a + n = m -> b + m = n -> n = mStructural proof guide
Generated structural guide
Opposing additive witnesses force equality.
Use the direct prerequisites add_assoc, drop_add_prefix_from_fixed as previously established PA formulas.
The proof proceeds by equality transport (4).
Referenced ingredients
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Linked names are exact direct references. This Stable checked-use theorem is independently kernel-checked when replayed.
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 assumptionsL1–6
02Calculate and transport equalitiesL7–8
03Use earlier factsL9–15
Instantiate or apply named facts and discharge the corresponding proof obligations.
Original exact command ledger · 19 lines
- 0001
intro a - 0002
intro b - 0003
intro n - 0004
intro m - 0005
intro h_anm - 0006
intro h_bmn - 0007
symm - 0008
rewrite <- h_anm - 0009
specialize drop_add_prefix_from_fixed a - 0010
specialize drop_add_prefix_from_fixed b - 0011
specialize drop_add_prefix_from_fixed n - 0012
apply drop_add_prefix_from_fixed - 0013
specialize add_assoc b - 0014
specialize add_assoc a - 0015
specialize add_assoc n - 0016
rewrite add_assoc - 0017
rewrite h_anm - 0018
rewrite h_bmn - 0019
refl