U32alg.add_cancel_r: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend as U32alg
Lines 25-30 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend&start_line=25&end_line=30

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

def add_cancel_r(+a: Nat, +b: Nat, +c: Nat, +e: {Nat.add(a, c) == Nat.add(b, c) : Nat}) -> {a == b : Nat}:
  match c:
    case 0n:
      Equal.trans(Nat, a, Nat.add(a, 0n), b, Equal.sym(Nat, Nat.add(a, 0n), a, N.add_zero(a)), Equal.trans(Nat, Nat.add(a, 0n), Nat.add(b, 0n), b, e, N.add_zero(b)))
    case 1n+k:
      add_cancel_r(a, b, k, N.succ_inj(Nat.add(a, k), Nat.add(b, k), Equal.trans(Nat, 1n+Nat.add(a, k), Nat.add(a, 1n+k), 1n+Nat.add(b, k), Equal.sym(Nat, Nat.add(a, 1n+k), 1n+Nat.add(a, k), N.add_succ(a, k)), Equal.trans(Nat, Nat.add(a, 1n+k), Nat.add(b, 1n+k), 1n+Nat.add(b, k), e, N.add_succ(b, k)))))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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-math@1.0.0.0/proofs/lib/nat.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=succ_inj