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
32 * 32 = 2 * (16 * 32)Structural proof guide
The root-32 square identity carried by the shallow factorization 16*32.
Direct prerequisites: scaled_factor_square_identity. The authored body proceeds by intermediate claims (1), closed numeral normalization (1).
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 (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 exact 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