Peth.words_v: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/peth.bend as Peth
Lines 17-31 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/peth.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/peth.bend&start_line=17&end_line=31

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend as CV
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/ecdsa.bend as ES
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/bytes.bend as B
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend as E
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/blist.bend as BL

def words_v(n: Nat, +bs: List<&2, U32>) -> {E.words(n, bs) == ES.words(n, bs) : List<&2, U32>}:
  match n:
    case 0n:
      {==}
    case 1n+ +k:
      %Equal.sym(List<&2, U32>, B.tail(bs), CV.after(1n, bs), BL.tail_after(bs)) : {E.word(B.head(bs), B.head(_), B.head(B.suffix(2n, bs)), B.head(B.suffix(3n, bs))) <> E.words(k, B.suffix(4n, bs)) == ES.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), CV.head(CV.after(3n, bs))) <> ES.words(k, CV.after(4n, bs)) : List<&2, U32>}
      %Equal.sym(List<&2, U32>, B.suffix(2n, bs), CV.after(2n, bs), BL.suffix_after(2n, bs)) : {E.word(B.head(bs), B.head(CV.after(1n, bs)), B.head(_), B.head(B.suffix(3n, bs))) <> E.words(k, B.suffix(4n, bs)) == ES.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), CV.head(CV.after(3n, bs))) <> ES.words(k, CV.after(4n, bs)) : List<&2, U32>}
      %Equal.sym(List<&2, U32>, B.suffix(3n, bs), CV.after(3n, bs), BL.suffix_after(3n, bs)) : {E.word(B.head(bs), B.head(CV.after(1n, bs)), B.head(CV.after(2n, bs)), B.head(_)) <> E.words(k, B.suffix(4n, bs)) == ES.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), CV.head(CV.after(3n, bs))) <> ES.words(k, CV.after(4n, bs)) : List<&2, U32>}
      %Equal.sym(List<&2, U32>, B.suffix(4n, bs), CV.after(4n, bs), BL.suffix_after(4n, bs)) : {E.word(B.head(bs), B.head(CV.after(1n, bs)), B.head(CV.after(2n, bs)), B.head(CV.after(3n, bs))) <> E.words(k, _) == ES.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), CV.head(CV.after(3n, bs))) <> ES.words(k, CV.after(4n, bs)) : List<&2, U32>}
      %Equal.sym(U32, B.head(bs), CV.head(bs), BL.head_eq(bs)) : {E.word(_, B.head(CV.after(1n, bs)), B.head(CV.after(2n, bs)), B.head(CV.after(3n, bs))) <> E.words(k, CV.after(4n, bs)) == ES.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), CV.head(CV.after(3n, bs))) <> ES.words(k, CV.after(4n, bs)) : List<&2, U32>}
      %Equal.sym(U32, B.head(CV.after(1n, bs)), CV.head(CV.after(1n, bs)), BL.head_eq(CV.after(1n, bs))) : {E.word(CV.head(bs), _, B.head(CV.after(2n, bs)), B.head(CV.after(3n, bs))) <> E.words(k, CV.after(4n, bs)) == ES.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), CV.head(CV.after(3n, bs))) <> ES.words(k, CV.after(4n, bs)) : List<&2, U32>}
      %Equal.sym(U32, B.head(CV.after(2n, bs)), CV.head(CV.after(2n, bs)), BL.head_eq(CV.after(2n, bs))) : {E.word(CV.head(bs), CV.head(CV.after(1n, bs)), _, B.head(CV.after(3n, bs))) <> E.words(k, CV.after(4n, bs)) == ES.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), CV.head(CV.after(3n, bs))) <> ES.words(k, CV.after(4n, bs)) : List<&2, U32>}
      %Equal.sym(U32, B.head(CV.after(3n, bs)), CV.head(CV.after(3n, bs)), BL.head_eq(CV.after(3n, bs))) : {E.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), _) <> E.words(k, CV.after(4n, bs)) == ES.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), CV.head(CV.after(3n, bs))) <> ES.words(k, CV.after(4n, bs)) : List<&2, U32>}
      %Equal.sym(List<&2, U32>, E.words(k, CV.after(4n, bs)), ES.words(k, CV.after(4n, bs)), words_v(k, CV.after(4n, bs))) : {E.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), CV.head(CV.after(3n, bs))) <> _ == ES.word(CV.head(bs), CV.head(CV.after(1n, bs)), CV.head(CV.after(2n, bs)), CV.head(CV.after(3n, bs))) <> ES.words(k, CV.after(4n, bs)) : List<&2, U32>}
      {==}

Uses (16):
  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=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/blist.bend&name=head_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/blist.bend&name=suffix_after
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/blist.bend&name=tail_after
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=after
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=head
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/ecdsa.bend&name=word
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/ecdsa.bend&name=words
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/bytes.bend&name=head
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/bytes.bend&name=suffix
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/bytes.bend&name=tail
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend&name=word
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend&name=words