Limbs.carry_ok: 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 263-279 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=263&end_line=279

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
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/word.bend as WD

# every output limb below 2^8, the same count
def carry_ok(+one: Nat, +h1: {one == 1n : Nat}, +n: Nat, +xs: List<&2, U32>, +c: U32, +hn: {okb(n, xs, WD.sc(28n, one)) == True{} : Bool}, +hc: {Nat.is_le(v(c), WD.sc(21n, one)) == True{} : Bool}) -> {okb(n, cl(F.carry(xs, c)), 255n) == True{} : Bool}:
  match n xs:
    case 0n Nil{}:
      {==}
    case 0n Con{y, yt}:
      Empty.absurd({okb(0n, cl(F.carry(Con{y, yt}, c)), 255n) == True{} : Bool}, L.false_true(hn))
    case 1n+m Nil{}:
      Empty.absurd({okb(1n+m, cl(F.carry(Nil{}, c)), 255n) == True{} : Bool}, L.false_true(hn))
    case 1n+ +m Con{+h, +t}:
      +hh = okb_head(m, h, t, WD.sc(28n, one), hn)
      +ht = okb_tail(m, h, t, WD.sc(28n, one), hn)
      +s = U32.add(h, c)
      +lo = U32.mod(s, 256)
      +r = F.carry(t, U32.div(s, 256))
      %Equal.sym(List<&2, U32>, cl(F.carry_con(lo, r)), Con{lo, cl(r)}, cl_con(lo, r)) : {okb(1n+m, _, 255n) == True{} : Bool}
      L.and_intro(Nat.is_le(v(lo), 255n), okb(m, cl(r), 255n), lo_le(s), carry_ok(one, h1, m, t, U32.div(s, 256), ht, c_next(one, h1, h, c, hh, hc)))

Uses (23):
  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.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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=c_next
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=cl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=cl_con
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=lo_le
  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_head
  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/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=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=carry
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=carry_con