BT0072

parity_cases

Stable ยท empty-context checked

Every natural has a constructive even-or-odd witness.

Exact expanded PA statement

forall n. exists k. n = 2 * k \/ n = 2 * k + 1

Structural proof guide

Every natural has a constructive even-or-odd witness.

Direct prerequisites: none. The authored body proceeds by structural induction (1), case analysis (2), equality transport (2), closed numeral normalization (1).

Proof neighborhood

Direct dependencies

none

Direct dependents

Formal native tactic body

Dependencies are hypotheses of this body receipt. The focused endpoint audits separately check the complete empty-context certificates.

  1. 0001induction n
  2. 0002exists 0
  3. 0003left
  4. 0004norm_num
  5. 0005cases IH
  6. 0006cases IH_witness
  7. 0007exists x
  8. 0008right
  9. 0009rewrite IH_witness_left
  10. 0010simp
  11. 0011exists x + 1
  12. 0012left
  13. 0013rewrite IH_witness_right
  14. 0014simp