PROOF.un.add_nowrap: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 650-656 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=650&end_line=656

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U
import bend-osdev-u32@0.1.0.0/LAWS.bend as Laws

def un.add_nowrap(c: Bool, +n: Nat, +s: Nat, +a: Nat, +b: Nat, +z: Nat, e: {Nat.add(s, U.U32Nat.dbl(n, U.U32Nat.bit(c))) == Nat.add(a, b) : Nat}, h: {Nat.is_le(Nat.add(a, b), z) == True{} : Bool}, hz: {Nat.is_lt(z, U.U32Nat.dbl(n, 1n)) == True{} : Bool}) -> {s == Nat.add(a, b) : Nat}:
  match c:
    case True{}:
      +k = U.U32Nat.dbl(n, 1n)
      Empty.absurd({s == Nat.add(a, b) : Nat}, un.add_lt_absurd(s, k, un.lt_rw(Nat.add(a, b), Nat.add(s, k), k, Equal.sym(Nat, Nat.add(s, k), Nat.add(a, b), e), un.le_lt_trans(Nat.add(a, b), z, k, h, hz))))
    case False{}:
      Equal.trans(Nat, s, Nat.add(s, 0n), Nat.add(a, b), Equal.sym(Nat, Nat.add(s, 0n), s, un.add_zero(s)), Equal.trans(Nat, Nat.add(s, 0n), Nat.add(s, U.U32Nat.dbl(n, 0n)), Nat.add(a, b), Equal.cong(Nat, Nat, v => Nat.add(s, v), 0n, U.U32Nat.dbl(n, 0n), Equal.sym(Nat, U.U32Nat.dbl(n, 0n), 0n, Laws.dbl_zero(n))), e))

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=dbl_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.add_lt_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.le_lt_trans
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.lt_rw
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.bit
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl