BT00WY · Bertrand theorem

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.

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

none

0 occurrences

In local proof propositions

none

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

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.

Definition notation is shown below. Open the paired exact edition for the original native formulas. Source pairing is not a new equivalence certificate.

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 defined 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