ProofShift.ns.double_add: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 51-56 of bend-osdev-word64@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&start_line=51&end_line=56

import Base
import bend-osdev-word64@0.1.1.0/proof_value.bend as P

def ns.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:
      P.wn.succ_cong(1n+Nat.double(Nat.add(p, y)), 1n+Nat.add(Nat.double(p), Nat.double(y)), P.wn.succ_cong(Nat.double(Nat.add(p, y)), Nat.add(Nat.double(p), Nat.double(y)), ns.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-word64@0.1.1.0/proof_value.bend&name=wn.succ_cong