PA0058

successor_odd_of_even

Stable checked-use theorem · independently closed

The successor of an even natural is odd.

Exact expanded PA statement

forall n. (exists a. n = 2 * a) -> exists b. S n = 2 * b + 1

Structural proof guide

Generated structural guide

The successor of an even natural is odd.

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

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

Referenced ingredients

none

Proof neighborhood

Direct dependencies

none

Direct dependents

PA005A even_successor_to_odd

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 n
  2. 0002intro he
  3. 0003cases he
  4. 0004exists x
  5. 0005rewrite he_witness
  6. 0006simp