BT001E

lt_of_le_of_lt

Stable · empty-context checked

Weak order followed by strict order remains strict.

Exact expanded PA statement

forall a b c. (exists k. k + a = b) -> (exists k. k + S b = c) -> exists k. k + S a = c

Structural proof guide

Weak order followed by strict order remains strict.

Direct prerequisites: add_assoc. The authored body proceeds by case analysis (2), equality transport (2).

Proof neighborhood

Direct dependencies

BT0003 add_assoc

Direct dependents

BT00R9 square_lt_successor_square BT00YB division_first_two_of_two_three_range

Formal native tactic body

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

  1. 0001intro a
  2. 0002intro b
  3. 0003intro c
  4. 0004intro hab
  5. 0005intro hbc
  6. 0006cases hab
  7. 0007cases hbc
  8. 0008exists x1 + x
  9. 0009trans x1 + (x + S a)
  10. 0010apply add_assoc
  11. 0011rewrite PA4
  12. 0012rewrite hab_witness
  13. 0013exact hbc_witness