BackwardPROOF.add_succ: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend as BackwardPROOF
Lines 23-28 of bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend&start_line=23&end_line=28

import Base

def add_succ(+left: Nat, +right: Nat) -> {Nat.add(left, 1n+right) == 1n+Nat.add(left, right) : Nat}:
  match left:
    case 0n:
      {==}
    case 1n+rest:
      Equal.cong(Nat, Nat, number => 1n+number, Nat.add(rest, 1n+right), 1n+Nat.add(rest, right), add_succ(rest, right))

Uses (3):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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