BT000V

add_left_cancel

Stable · empty-context checked

A common left addend can be cancelled.

Exact expanded PA statement

forall a b c. a + b = a + c -> b = c

Structural proof guide

A common left addend can be cancelled.

Direct prerequisites: add_comm, add_right_cancel. The authored body proceeds by direct introduction and elimination.

Proof neighborhood

Direct dependencies

BT0002 add_comm BT000U add_right_cancel

Direct dependents

BT001S positive_quotient_gap_impossible BT001U division_remainder_unique BT00RG double_triple_remainder_complement_budget BT00VE primorial_interval_pairwise_coprime BT00XC add_lt_cancel_left BT00Y4 central_binom_carry_bit_count

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 h
  5. 0005specialize add_right_cancel b
  6. 0006specialize add_right_cancel c
  7. 0007specialize add_right_cancel a
  8. 0008apply add_right_cancel
  9. 0009trans a + b
  10. 0010apply add_comm
  11. 0011trans a + c
  12. 0012exact h
  13. 0013apply add_comm