Bytes.bitlen_okb: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/bytes.bend as Bytes
Lines 92-101 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/bytes.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/bytes.bend&start_line=92&end_line=101

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/x25519.bend as X
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/crypto/curve25519/limbs.bend as LM

def bitlen_okb(+n: Nat, +xs: List<&2, U32>, +b: Nat, +e: {LM.okb(n, xs, b) == True{} : Bool}) -> {X.bitlen(xs) == e8(n) : Nat}:
  match n xs:
    case 0n Nil{}:
      {==}
    case 0n Con{x, xt}:
      Empty.absurd({X.bitlen(Con{x, xt}) == 0n : Nat}, L.true_false(Equal.sym(Bool, False{}, True{}, e)))
    case 1n+k Nil{}:
      Empty.absurd({0n == e8(1n+k) : Nat}, L.true_false(Equal.sym(Bool, False{}, True{}, e)))
    case 1n+ +k Con{+x, +xt}:
      Equal.cong(Nat, Nat, z => Nat.add(8n, z), X.bitlen(xt), e8(k), bitlen_okb(k, xt, b, L.and_right(Nat.is_le(v(x), b), LM.okb(k, xt, b), e)))

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=Equal.cong
  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=Nat.add
  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=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/ed25519/bytes.bend&name=e8
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/bytes.bend&name=v
  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=true_false
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/x25519.bend&name=bitlen