PA006U

even_mul_left

Stable checked-use theorem · independently closed

A product with an even left factor is even.

Exact expanded PA statement

forall m n. (exists a. m = 2 * a) -> exists c. m * n = 2 * c

Structural proof guide

Generated structural guide

A product with an even left factor is even.

Use the direct prerequisites mul_assoc as previously established PA formulas.

The proof proceeds by case analysis (1), equality transport (1).

Referenced ingredients

PA000B mul_assoc

Proof neighborhood

Direct dependencies

PA000B mul_assoc

Direct dependents

PA00FO qres_same_status_from_mod_four_one

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Linked names are exact direct references. This Stable checked-use theorem is independently kernel-checked when replayed.

  1. 0001intro m
  2. 0002intro n
  3. 0003intro hm
  4. 0004cases hm
  5. 0005exists x * n
  6. 0006rewrite hm_witness
  7. 0007apply mul_assoc