PA005B

successor_even_of_odd

Stable checked-use theorem · independently closed

The successor of an odd natural is even.

Exact expanded PA statement

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

Structural proof guide

Generated structural guide

The successor of an odd natural is even.

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

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 ho
  3. 0003cases ho
  4. 0004exists x + 1
  5. 0005rewrite ho_witness
  6. 0006simp