Mulw.cb_okb: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/mulw.bend as Mulw
Lines 47-56 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/mulw.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/mulw.bend&start_line=47&end_line=56

import Base
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/num.bend as M
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/poly.bend as PL

def cb_okb(+n: Nat, +xs: List<&2, U32>, +b: Nat, +k: Nat, +e: {LM.okb(n, xs, b) == True{} : Bool}) -> {PL.cb(xs, k) == PL.cbn(n, k) : Nat}:
  match n xs:
    case 0n Nil{}:
      {==}
    case 0n Con{y, yt}:
      Empty.absurd({PL.cb(Con{y, yt}, k) == 0n : Nat}, L.false_true(e))
    case 1n+m Nil{}:
      Empty.absurd({0n == PL.cbn(1n+m, k) : Nat}, L.false_true(e))
    case 1n+ +m Con{+y, +yt}:
      M.cong_r(k, PL.cb(yt, k), PL.cbn(m, k), cb_okb(m, yt, b, k, LM.okb_tail(m, y, yt, b, e)))

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=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=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=okb_tail
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend&name=cong_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/poly.bend&name=cb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/poly.bend&name=cbn
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true