Reduce.canon_lb: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend as Reduce
Lines 262-273 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend&start_line=262&end_line=273

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bounds.bend as B

def canon_lb(+one: Nat, +h1: {one == 1n : Nat}, +c: List<&2, Nat>, +t: List<&2, Nat>, +ht16: {FS.limbs16(one, 16n, t) == True{} : Bool}, b: Nat, +hb: {Nat.is_lt(b, 2n) == True{} : Bool}) -> {FS.limbs16(one, 16n, L.select(b, L.take(16n, L.carry(32n, L.add(t, c), 0n)), t)) == True{} : Bool}:
  match b:
    case 0n:
      +hu16 = B.carry_limbs(one, h1, 32n, 16n, L.add(t, c), 0n, {==})
      %Equal.sym(List<&2, Nat>, L.select(0n, L.take(16n, L.carry(32n, L.add(t, c), 0n)), t), t, sel_zero(one, 16n, L.take(16n, L.carry(32n, L.add(t, c), 0n)), t, hu16, ht16)) : {FS.limbs16(one, 16n, _) == True{} : Bool}
      ht16
    case 1n:
      +hu16 = B.carry_limbs(one, h1, 32n, 16n, L.add(t, c), 0n, {==})
      %Equal.sym(List<&2, Nat>, L.select(1n, L.take(16n, L.carry(32n, L.add(t, c), 0n)), t), L.take(16n, L.carry(32n, L.add(t, c), 0n)), sel_one(one, 16n, L.take(16n, L.carry(32n, L.add(t, c), 0n)), t, hu16, ht16)) : {FS.limbs16(one, 16n, _) == True{} : Bool}
      hu16
    case 2n+ +k:
      Empty.absurd({FS.limbs16(one, 16n, L.select(2n+k, L.take(16n, L.carry(32n, L.add(t, c), 0n)), t)) == True{} : Bool}, N.lt_zero_absurd(k, hb))

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.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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bounds.bend&name=carry_limbs
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend&name=sel_one
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend&name=sel_zero
  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/spec/crypto/secp256k1/field.bend&name=limbs16
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=carry
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=select
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=take