PROOF.un.sub_mid: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 673-679 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=673&end_line=679

import Base

# (1 + (a + nb)) + b = a + k when 1 + nb + b = k
def un.sub_mid(a: Nat, -nb: Nat, -b: Nat, -k: Nat, en: {1n+Nat.add(nb, b) == k : Nat}) -> {Nat.add(1n+Nat.add(a, nb), b) == Nat.add(a, k) : Nat}:
  match a:
    case 0n:
      en
    case 1n+p:
      un.succ_cong(Nat.add(1n+Nat.add(p, nb), b), Nat.add(p, k), un.sub_mid(p, nb, b, k, en))

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-osdev-u32@0.1.0.0/PROOF.bend&name=un.succ_cong