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.
Statement with defined notation
forall a b n m. a + n = m -> b + m = n -> n = mEvery purple notation token opens its conservative definition. This is a reading surface; the compiler expands the statement before the unchanged kernel checks it.
Definitions used by this theorem
In the theorem statement
0 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall a b n m. a + n = m -> b + m = n -> n = mProof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only local propositions introduced by have or suffices are compacted. The untrusted compiler re-expands each one before the original tactic script is replayed; defined notation is never accepted by the kernel. Open the exact replay line beneath every changed command.
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 defined 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