BT00WY

thirty_two_square_eq_twice_sixteen_times_thirty_two

Alpha v34 checked-use theorem · independently kernel and Lean verified; not Stable

The root-32 square identity carried by the shallow factorization 16*32.

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

7 script commands · 1 reading checkpoints · 1 local claims

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.

  1. L1
    have hfactor : 32 = 2 * 16
  2. L2
    norm_num
  3. L3
    specialize scaled_factor_square_identity 2
  4. L4
    specialize scaled_factor_square_identity 16
  5. L5
    specialize scaled_factor_square_identity 32
  6. L6
    apply scaled_factor_square_identity
  7. L7
    exact hfactor

Library-wide reading audit

Original exact command ledger · 7 lines
  1. 0001have hfactor : 32 = 2 * 16
  2. 0002norm_num
  3. 0003specialize scaled_factor_square_identity 2
  4. 0004specialize scaled_factor_square_identity 16
  5. 0005specialize scaled_factor_square_identity 32
  6. 0006apply scaled_factor_square_identity
  7. 0007exact hfactor