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
32 * 32 = 2 * (16 * 32)Every purple notation token opens its conservative definition. Expanding the displayed statement recovers the exact first-order Peano-arithmetic formula checked by the unchanged kernel.
Definitions used by this theorem
In the theorem statement
0 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
32 * 32 = 2 * (16 * 32)Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only local propositions introduced by have or suffices are compacted. Every changed line has an exact-AST conservative-expansion receipt; the kernel still receives the immutable original tactic script.
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 (1)
01Establish hfactorL1–7
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply scaled factor square identity.
Original defined command ledger · 7 lines
- 0001
have hfactor : 32 = 2 * 16 - 0002
norm_num - 0003
specialize scaled_factor_square_identity 2 - 0004
specialize scaled_factor_square_identity 16 - 0005
specialize scaled_factor_square_identity 32 - 0006
apply scaled_factor_square_identity - 0007
exact hfactor