ProofU32.uq.val_lt: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/proof_u32.bend as ProofU32
Lines 150-159 of bend-osdev-algo@0.1.0.0/proof_u32.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/proof_u32.bend&start_line=150&end_line=159

import Base

def uq.val_lt(n: Nat, w: Word(n)) -> {Nat.is_lt(Word.to_nat(n, w), uq.pw(n)) == True{} : Bool}:
  match n:
    case 0n:
      {==}
    case 1n+ +p:
      match w:
        case WCon{False{}, +t}:
          Equal.trans(Bool, Nat.is_lt(Nat.double(Word.to_nat(p, t)), Nat.double(uq.pw(p))), Nat.is_lt(Word.to_nat(p, t), uq.pw(p)), True{}, uq.lt_dbl(Word.to_nat(p, t), uq.pw(p)), uq.val_lt(p, t))
        case WCon{True{}, +t}:
          Equal.trans(Bool, Nat.is_lt(1n+Nat.double(Word.to_nat(p, t)), Nat.double(uq.pw(p))), Nat.is_lt(Word.to_nat(p, t), uq.pw(p)), True{}, uq.lt_dbl1(Word.to_nat(p, t), uq.pw(p)), uq.val_lt(p, t))

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.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=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.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_u32.bend&name=uq.lt_dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_u32.bend&name=uq.lt_dbl1
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_u32.bend&name=uq.pw