PROOF.un.double_add: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 83-88 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=83&end_line=88

import Base

def un.double_add(x: Nat, -y: Nat) -> {Nat.double(Nat.add(x, y)) == Nat.add(Nat.double(x), Nat.double(y)) : Nat}:
  match x:
    case 0n:
      {==}
    case 1n+p:
      un.succ_cong(1n+Nat.double(Nat.add(p, y)), 1n+Nat.add(Nat.double(p), Nat.double(y)), un.succ_cong(Nat.double(Nat.add(p, y)), Nat.add(Nat.double(p), Nat.double(y)), un.double_add(p, y)))

Uses (4):
  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.double
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.succ_cong