Bytes.below_take: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/random/bytes.bend as Bytes
Lines 162-170 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/random/bytes.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/random/bytes.bend&start_line=162&end_line=170

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/random.bend as SCR
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L

def below_take(+n: Nat, +xs: List<&2, U32>, +h: {SCR.below256(xs) == True{} : Bool}) -> {SCR.below256(SCR.take(n, xs)) == True{} : Bool}:
  match n xs:
    case 0n _:
      {==}
    case 1n+p Nil{}:
      {==}
    case 1n+p Con{+x, +rest}:
      %Equal.sym(Bool, U32.is_lt(x, 256), True{}, L.and_left(U32.is_lt(x, 256), SCR.below256(rest), h)) : {Bool.and(_, SCR.below256(SCR.take(p, rest))) == True{} : Bool}
      below_take(p, rest, L.and_right(U32.is_lt(x, 256), SCR.below256(rest), h))

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=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  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/spec/crypto/random.bend&name=below256
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/random.bend&name=take