ProofU32.dm_rec: def of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_u32.bend as ProofU32
Lines 783-797 of lawful-words@0.1.0.0/proof_u32.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_u32.bend&start_line=783&end_line=797

import Base
import lawful-words@0.1.0.0/proof_nat.bend as N
import lawful-words@0.1.0.0/proof_word.bend as W

def dm_rec(+p: Nat, +a0: Bool, +hi: Word(p), +b: U32, +m: Nat, +hm: {Nat.pow(2n, 32n) == m : Nat},
  qr: Word(p) & U32, ih: DMOK(p, Word.to_nat(p, hi), U32.to_nat(b), qr)) ->
  DMOK(1n+p, Word.to_nat(1n+p, WCon{a0, hi}), U32.to_nat(b), U32.divmod.go.rec(p, a0, b, qr)):
  match qr:
    case (+q, +r):
      match r:
        case U32{+rw}:
          match ih:
            case (+e1, +e2):
              %Equal.sym(Nat, Word.to_nat(1n+p, WCon{a0, hi}), Nat.add(N.bn(a0), Nat.double(Word.to_nat(p, hi))), W.wcon(p, a0, hi)) :
                DMOK(1n+p, _, U32.to_nat(b), U32.divmod.go.rec(p, a0, b, (q, U32{rw})))
              %Equal.sym(Bool & Word(32n), Word.shl.out(32n, a0, rw), (W.stop(32n, a0, rw), Word.shl.put(32n, a0, rw)), shl_out(32n, a0, rw)) :
                DMOK(1n+p, Nat.add(N.bn(a0), Nat.double(Word.to_nat(p, hi))), U32.to_nat(b), U32.divmod.go.shl(p, q, b, _))
              dm_fin.t(p, q, Word.shl.put(32n, a0, rw), W.stop(32n, a0, rw), b, a0, hi, Word.to_nat(32n, rw), m, hm,
                Bool.or(W.stop(32n, a0, rw), U32.is_ge(U32{Word.shl.put(32n, a0, rw)}, b)), {==}, e1, e2, wput.m(a0, rw, m, hm))

Uses (26):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  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=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=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.divmod.go.shl
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_ge
  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=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shl.out
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shl.put
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=bn
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=DMOK
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=dm_fin.t
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=shl_out
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=wput.m
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_word.bend&name=stop
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_word.bend&name=wcon