PROOF.na.sub_add: def of bend-osdev-cipher-modes@0.1.0.0
Import: import bend-osdev-cipher-modes@0.1.0.0/PROOF.bend as PROOF
Lines 1684-1692 of bend-osdev-cipher-modes@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&start_line=1684&end_line=1692

import Base

# (a + b) - b == a
def na.sub_add(+a: Nat, +b: Nat) -> {Nat.sub(Nat.add(a, b), b) == a : Nat}:
  match b:
    case 0n:
      %Equal.sym(Nat, Nat.add(a, 0n), a, na.add_zero(a)) : {Nat.sub(_, 0n) == a : Nat}
      na.sub_zero(a)
    case 1n+p:
      %Equal.sym(Nat, Nat.add(a, 1n+p), 1n+Nat.add(a, p), na.add_succ(a, p)) : {Nat.sub(_, 1n+p) == a : Nat}
      na.sub_add(a, 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=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-cipher-modes@0.1.0.0/PROOF.bend&name=na.add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=na.add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=na.sub_zero