UniqueProofs.cancel_right: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/shape/unique_proofs.bend as UniqueProofs
Lines 23-28 of bendtorch-core@0.1.0.0/src/shape/unique_proofs.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/shape/unique_proofs.bend&start_line=23&end_line=28

import Base
import bendtorch-core@0.1.0.0/src/shape/broadcast_proofs.bend as Broadcast

def cancel_right(+a: Nat, +b: Nat, +c: Nat, equal: {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, Broadcast.add_zero(a)), Equal.trans(Nat, Nat.add(a, 0n), Nat.add(b, 0n), b, equal, Broadcast.add_zero(b)))
    case 1n+p:
      cancel_right(a, b, p, succ_injective(Nat.add(a, p), Nat.add(b, p), Equal.trans(Nat, 1n+Nat.add(a, p), Nat.add(a, 1n+p), 1n+Nat.add(b, p), Broadcast.add_succ(a, p), Equal.trans(Nat, Nat.add(a, 1n+p), Nat.add(b, 1n+p), 1n+Nat.add(b, p), equal, Equal.sym(Nat, 1n+Nat.add(b, p), Nat.add(b, 1n+p), Broadcast.add_succ(b, p))))))

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=bendtorch-core@0.1.0.0/src/shape/broadcast_proofs.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/broadcast_proofs.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/unique_proofs.bend&name=succ_injective