Phc.sd_dec: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/phc.bend as Phc
Lines 1288-1296 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/phc.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/phc.bend&start_line=1288&end_line=1296

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/phc.bend as PH

def sd_dec(+f: Nat, +n: Nat, +acc: String, +Y: String, +last: Bool, +el: {Nat.is_lt(n, 10n) == last : Bool}, +hf: {Nat.is_lt(n, f) == True{} : Bool}) -> {PH.starts_digit(String.append(PH.dec_go(f, n, acc, last), Y)) == True{} : Bool}:
  match f last:
    case 0n _:
      Empty.absurd({PH.starts_digit(String.append(acc, Y)) == True{} : Bool}, N.lt_zero_absurd(n, hf))
    case 1n+ +g True{}:
      di_n(n, el)
    case 1n+ +g False{}:
      +q = Nat.div(n, 10n)
      sd_dec(g, q, SCon{PH.dchar(Nat.mod(n, 10n)), acc}, Y, Nat.is_lt(q, 10n), {==}, N.lt_le_trans(q, n, g, div10_lt(n, ge10_pos(n, el)), N.lt_succ_le(n, g, hf)))

Uses (17):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.div
  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=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=String
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=String.append
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/phc.bend&name=di_n
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/phc.bend&name=div10_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/phc.bend&name=ge10_pos
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_le_trans
  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/proofs/lib/nat.bend&name=lt_zero_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/phc.bend&name=dchar
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/phc.bend&name=dec_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/phc.bend&name=starts_digit