Lits.lits16_w: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/lits.bend as Lits
Lines 35-47 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/lits.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/lits.bend&start_line=35&end_line=47

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
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/proofs/lib/logic.bend as Lg

def lits16_w(+one: Nat, +h1: {one == 1n : Nat}, +w: Nat, +hw: {C.shift(10n, one) == w : Nat}, n: Nat, xs: List<&2, Nat>, +h: {ok16(w, n, xs) == True{} : Bool}) -> {FS.limbs16(one, n, xs) == True{} : Bool}:
  match n xs:
    case 0n Nil{}:
      {==}
    case 0n x <> t:
      Empty.absurd({FS.limbs16(one, 0n, x <> t) == True{} : Bool}, Lg.false_true(h))
    case 1n+k Nil{}:
      Empty.absurd({FS.limbs16(one, 1n+k, []) == True{} : Bool}, Lg.false_true(h))
    case 1n+ +k +x <> +t:
      +q = Nat.add(Nat.add(Nat.add(Nat.add(Nat.add(Nat.add(w, w), Nat.add(w, w)), Nat.add(Nat.add(w, w), Nat.add(w, w))), Nat.add(Nat.add(Nat.add(w, w), Nat.add(w, w)), Nat.add(Nat.add(w, w), Nat.add(w, w)))), Nat.add(Nat.add(Nat.add(Nat.add(w, w), Nat.add(w, w)), Nat.add(Nat.add(w, w), Nat.add(w, w))), Nat.add(Nat.add(Nat.add(w, w), Nat.add(w, w)), Nat.add(Nat.add(w, w), Nat.add(w, w))))), Nat.add(Nat.add(Nat.add(Nat.add(Nat.add(w, w), Nat.add(w, w)), Nat.add(Nat.add(w, w), Nat.add(w, w))), Nat.add(Nat.add(Nat.add(w, w), Nat.add(w, w)), Nat.add(Nat.add(w, w), Nat.add(w, w)))), Nat.add(Nat.add(Nat.add(Nat.add(w, w), Nat.add(w, w)), Nat.add(Nat.add(w, w), Nat.add(w, w))), Nat.add(Nat.add(Nat.add(w, w), Nat.add(w, w)), Nat.add(Nat.add(w, w), Nat.add(w, w))))))
      +hx = Lg.and_left(Nat.is_lt(x, q), ok16(w, k, t), h)
      +ht = Lg.and_right(Nat.is_lt(x, q), ok16(w, k, t), h)
      Lg.and_intro(Nat.is_lt(x, C.shift(16n, one)), FS.limbs16(one, k, t), lt16(one, h1, x, w, hw, hx), lits16_w(one, h1, w, hw, k, t, ht))

Uses (14):
  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=Nat.add
  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/lits.bend&name=lt16
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/lits.bend&name=ok16
  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=and_left
  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=false_true
  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/spec/lib/common.bend&name=shift