BT00VR

double_half_predecessor_data

Alpha body-checked ยท checked-use disabled

An even successor has a nonzero half below its predecessor.

Exact expanded PA statement

forall n k. S n = 2 * k -> (~(k = 0) /\ (exists bcf_le_gap_bdhpb_result. bcf_le_gap_bdhpb_result + (k) = n))

Structural proof guide

An even successor has a nonzero half below its predecessor.

Direct prerequisites: two_mul_eq_add_self, add_succ_left. The authored body proceeds by structural induction (1), closed numeral normalization (1).

Proof neighborhood

Direct dependencies

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. 0001intro n
  2. 0002induction k
  3. 0003intro heq
  4. 0004exfalso
  5. 0005apply PA1
  6. 0006trans 2 * 0
  7. 0007exact heq
  8. 0008norm_num
  9. 0009intro heq
  10. 0010split
  11. 0011intro hk
  12. 0012apply PA1
  13. 0013exact hk
  14. 0014exists k
  15. 0015apply PA2
  16. 0016trans 2 * S k
  17. 0017simp [two_mul_eq_add_self, add_succ_left]
  18. 0018symm
  19. 0019exact heq