PA001E

multiple_zero

Stable checked-use theorem · independently closed

Zero is a multiple of every natural number.

Exact expanded PA statement

forall a. exists q. 0 = a * q

Structural proof guide

Generated structural guide

Zero is a multiple of every natural number.

This root lemma is proved directly from the PA rules and the hypotheses introduced by its statement.

The proof proceeds by equality transport (1).

Referenced ingredients

none

Proof neighborhood

Direct dependencies

none

Direct dependents

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 a
  2. 0002exists 0
  3. 0003rewrite PA5
  4. 0004refl