Limbs.bytes_okb: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as Limbs
Lines 115-127 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&start_line=115&end_line=127

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
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

# the spec's tight (bytes_ok 32: limbs below 256) is okb 32 with bound 255
def bytes_okb(+n: Nat, +xs: List<&2, U32>, +e: {FS.bytes_ok(n, xs) == True{} : Bool}) -> {okb(n, xs, 255n) == True{} : Bool}:
  match n xs:
    case 0n Nil{}:
      {==}
    case 0n Con{y, yt}:
      Empty.absurd({okb(0n, Con{y, yt}, 255n) == True{} : Bool}, L.false_true(e))
    case 1n+m Nil{}:
      Empty.absurd({okb(1n+m, Nil{}, 255n) == True{} : Bool}, L.false_true(e))
    case 1n+ +m Con{+y, +yt}:
      +h = L.and_left(Nat.is_lt(v(y), 256n), FS.bytes_ok(m, yt), e)
      +t = L.and_right(Nat.is_lt(v(y), 256n), FS.bytes_ok(m, yt), e)
      L.and_intro(Nat.is_le(v(y), 255n), okb(m, yt, 255n), N.lt_succ_le(v(y), 255n, h), bytes_okb(m, yt, t))

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=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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=Base/base.bend&name=U32
  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/curve25519/limbs.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=and_left
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=and_right
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true
  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/spec/crypto/curve25519/field.bend&name=bytes_ok