BT004V

right_factor_divides_product

Stable checked-use theorem · independently kernel verified

The right factor divides a product.

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

forall a b. exists k. a * b = b * k

Structural proof guide

The right factor divides a product.

Direct prerequisites: mul_comm. The authored body proceeds by direct introduction and elimination.

Proof neighborhood

Direct dependencies

BT0006 mul_comm

Direct dependents

BT0059 beta_exclusive_accumulated_product_step

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

4 script commands · 3 reading checkpoints · 0 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)
mul comm
01Fix variables and assumptionsL1–2

Work with arbitrary variables or the premises of the current implication.

  1. L1
    intro a
  2. L2
    intro b
02Construct an explicit witnessL3–3

Supply the displayed value, then prove that it has the required property.

  1. L3
    exists a
03Use earlier factsL4–4

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L4
    apply mul_comm

Library-wide reading audit

Original exact command ledger · 4 lines
  1. 0001intro a
  2. 0002intro b
  3. 0003exists a
  4. 0004apply mul_comm