Limbs.pos_add: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as Limbs
Lines 110-117 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&start_line=110&end_line=117

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as WW

def pos_add(n: Nat, +x: Nat, +y: Nat) -> {pos(n, Nat.add(x, y)) == Nat.add(pos(n, x), pos(n, y)) : Nat}:
  match n:
    case 0n:
      {==}
    case 1n+ +k:
      %Equal.sym(Nat, pos(k, Nat.add(x, y)), Nat.add(pos(k, x), pos(k, y)), pos_add(k, x, y)) : {C.shift(16n, _) == Nat.add(C.shift(16n, pos(k, x)), C.shift(16n, pos(k, y))) : Nat}
      %Equal.sym(Nat, C.shift(16n, Nat.add(pos(k, x), pos(k, y))), Nat.add(C.shift(16n, pos(k, x)), C.shift(16n, pos(k, y))), WW.shift_add(16n, pos(k, x), pos(k, y))) : {_ == Nat.add(C.shift(16n, pos(k, x)), C.shift(16n, pos(k, y))) : Nat}
      {==}

Uses (6):
  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=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=pos
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend&name=shift_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift