U32.internal_inc_core: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 387-399 of bend-mathlib@0.8.1.0/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/u32.bend&start_line=387&end_line=399

import Base
import bend-mathlib@0.8.1.0/nat.bend as MNat

def internal_inc_core(n: Nat, w: Word(n)) -> {Nat.add(Word.to_nat(n, Word.inc(n, w)), Bool.pick(Nat, internal_inc_carry(n, w), Nat.pow(2n, n), 0n)) == 1n+Word.to_nat(n, w) : Nat}:
  match n:
    case 0n:
      {==}
    case 1n++p:
      match w:
        case WCon{False{}, t}:
          MNat.add_zero(1n+Nat.double(Word.to_nat(p, t)))
        case WCon{True{}, +t}:
          -x = Word.to_nat(p, t)
          %internal_pick_pow(internal_inc_carry(p, t), p) : {Nat.add(Nat.double(Word.to_nat(p, Word.inc(p, t))), _) == 2n+Nat.double(x) : Nat}
          %MNat.double_add(Word.to_nat(p, Word.inc(p, t)), Bool.pick(Nat, internal_inc_carry(p, t), Nat.pow(2n, p), 0n)) : {_ == 2n+Nat.double(x) : Nat}
          Equal.cong(Nat, Nat, z => Nat.double(z), Nat.add(Word.to_nat(p, Word.inc(p, t)), Bool.pick(Nat, internal_inc_carry(p, t), Nat.pow(2n, p), 0n)), 1n+Word.to_nat(p, t), internal_inc_core(p, t))

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.pick
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.inc
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=double_add
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=internal_inc_carry
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=internal_pick_pow