NatOrder.successor: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 158-167 of stelliferous@0.0.2.0/proofs/nat_order.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&start_line=158&end_line=167

import Base
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding

def successor(+a: Nat,+b: Nat,h: {Nat.is_le(a,b) == True{} : Bool}) -> {Nat.is_le(a,1n+b) == True{} : Bool}:
  match a:
    case 0n:
      {==}
    case 1n+ +p:
      match b:
        case 0n:
          Empty.absurd({Nat.is_le(1n+p,1n) == True{} : Bool},WordEncoding.false_true(h))
        case 1n+q:
          successor(p,q,h)

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true