Pdec.le_bytes_ok: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/pdec.bend as Pdec
Lines 163-172 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/pdec.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/pdec.bend&start_line=163&end_line=172

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/x25519.bend as SX
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend as U
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as NR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM

def le_bytes_ok(+n: Nat, +x: Nat) -> {LM.okb(n, SX.le_bytes(n, x), 255n) == True{} : Bool}:
  match n:
    case 0n:
      {==}
    case 1n+ +m:
      +r = Nat.mod(x, 256n)
      +hr = NR.dm_lt(255n, x)
      +e = U.to_nat_from_nat(r, 8n, {==}, hr)
      +h = L.subst(Nat, z => {Nat.is_le(z, 255n) == True{} : Bool}, r, v(U32.from_nat(r)), Equal.sym(Nat, v(U32.from_nat(r)), r, e), N.lt_succ_le(r, 255n, hr))
      L.and_intro(Nat.is_le(v(U32.from_nat(r)), 255n), LM.okb(m, SX.le_bytes(m, Nat.div(x, 256n)), 255n), h, le_bytes_ok(m, Nat.div(x, 256n)))

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=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.div
  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.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=okb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/pdec.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=and_intro
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_succ_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&name=to_nat_from_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend&name=dm_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/x25519.bend&name=le_bytes