Arith.add_cancel: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as Arith
Lines 40-46 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend&start_line=40&end_line=46

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N

# c + a == c + b gives a == b   (Mathlib Nat.add_left_cancel)
def add_cancel(+c: Nat, +a: Nat, +b: Nat, +e: {Nat.add(c, a) == Nat.add(c, b) : Nat}) -> {a == b : Nat}:
  match c:
    case 0n:
      e
    case 1n+ +cp:
      add_cancel(cp, a, b, N.succ_inj(Nat.add(cp, a), Nat.add(cp, b), e))

Uses (3):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=succ_inj