PROOF.pk.add_sub: def of bend-osdev-pkcs7@0.1.0.0
Import: import bend-osdev-pkcs7@0.1.0.0/PROOF.bend as PROOF
Lines 48-56 of bend-osdev-pkcs7@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-pkcs7@0.1.0.0/PROOF.bend&start_line=48&end_line=56

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

# (L + k) - k is L
def pk.add_sub(+l: Nat, +k: Nat) -> {Nat.sub(Nat.add(l, k), k) == l : Nat}:
  match k:
    case 0n:
      %UL.nat_add_zero(l) : {Nat.sub(Nat.add(l, 0n), 0n) == _ : Nat}
      pk.sub_zero(Nat.add(l, 0n))
    case 1n+kp:
      %Equal.sym(Nat, Nat.add(l, 1n+kp), 1n+Nat.add(l, kp), UL.nat_add_succ(l, kp)) : {Nat.sub(_, 1n+kp) == l : Nat}
      pk.add_sub(l, kp)

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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-pkcs7@0.1.0.0/PROOF.bend&name=pk.sub_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_zero