EL000D

lte_nondivisor_product_right

Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable

Nondivisibility of a product excludes divisibility of its right factor.

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 first-order arithmetic statement

forall p a b. ~(exists olte_factor_product. (a * b) = (p) * olte_factor_product) -> ~(exists olte_factor_right. (b) = (p) * olte_factor_right)

Constructive proof overview

Generated structural guide

Nondivisibility of a product excludes divisibility of its right factor.

The unchanged tactic script uses 1 declared prerequisite and contains 11 exact native proof lines.

Alpha v34 checked-use · first admitted v29 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

multiple_mul_left Stable theorem; checked-use authorized

Direct dependents

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.

Read the argument

Proof checkpoints

11 script commands · 2 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.

01Fix variables and assumptionsL1–5

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

  1. L1
    intro p
  2. L2
    intro a
  3. L3
    intro b
  4. L4
    intro hnot
  5. L5
    intro hdiv
02Use earlier factsL6–11

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

  1. L6
    apply hnot
  2. L7
    specialize multiple_mul_left (p)
  3. L8
    specialize multiple_mul_left (b)
  4. L9
    specialize multiple_mul_left (a)
  5. L10
    apply multiple_mul_left
  6. L11
    exact hdiv

Library-wide reading audit

Original exact command ledger · 11 lines
  1. 0001intro p
  2. 0002intro a
  3. 0003intro b
  4. 0004intro hnot
  5. 0005intro hdiv
  6. 0006apply hnot
  7. 0007specialize multiple_mul_left (p)
  8. 0008specialize multiple_mul_left (b)
  9. 0009specialize multiple_mul_left (a)
  10. 0010apply multiple_mul_left
  11. 0011exact hdiv