PROOF.ud.step: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 1774-1782 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=1774&end_line=1782

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

def ud.step(+p: Nat, +a0: Bool, +b: U32, qr: Word(p) & U32, +x: Nat, +x2: Nat, +ex: {Nat.add(U.U32Nat.bit(a0), Nat.double(x)) == x2 : Nat}, ih: {Nat.add(Nat.mul(ud.q(p, qr), U32.to_nat(b)), ud.r(p, qr)) == x : Nat} & {Nat.is_lt(ud.r(p, qr), U32.to_nat(b)) == True{} : Bool}) -> {Nat.add(Nat.mul(ud.q(1n+p, U32.divmod.go.rec(p, a0, b, qr)), U32.to_nat(b)), ud.r(1n+p, U32.divmod.go.rec(p, a0, b, qr))) == x2 : Nat} & {Nat.is_lt(ud.r(1n+p, U32.divmod.go.rec(p, a0, b, qr)), U32.to_nat(b)) == True{} : Bool}:
  match b:
    case U32{+bw}:
      match qr:
        case (+q, +r):
          match r:
            case U32{+rw}:
              (+i1, +i2) = ih
              ud.step2(p, a0, bw, q, rw, x, x2, ex, i1, i2)

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=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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.divmod.go.rec
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ud.q
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ud.r
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ud.step2
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.bit