Penc.rhs_v: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend as Penc
Lines 74-81 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend&start_line=74&end_line=81

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/spec/crypto/secp256k1/curve.bend as CV
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend as P
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend as FO
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT

def rhs_v(+one: Nat, +h1: {one == 1n : Nat}, +x: List<&2, Nat>, +hx: {PT.red(one, x) == True{} : Bool}) -> {FS.value(one, P.rhs(x)) == CV.rhs(FS.prime(one), FS.value(one, x)) : Nat}:
  +h2 = FO.mul_r(one, h1, x, x, hx, hx)
  +h3 = FO.mul_r(one, h1, F.mul(x, x), x, h2, hx)
  %Equal.sym(Nat, FS.value(one, F.add(F.mul(F.mul(x, x), x), F.small(7n))), FS.madd(FS.prime(one), FS.value(one, F.mul(F.mul(x, x), x)), FS.value(one, F.small(7n))), FO.add_v(one, h1, F.mul(F.mul(x, x), x), F.small(7n), h3, FO.small_r(one, h1, 7n, seven_lt(one, h1)))) : {_ == FS.madd(FS.prime(one), FS.mmul(FS.prime(one), FS.mmul(FS.prime(one), FS.value(one, x), FS.value(one, x)), FS.value(one, x)), 7n) : Nat}
  %Equal.sym(Nat, FS.value(one, F.mul(F.mul(x, x), x)), FS.mmul(FS.prime(one), FS.value(one, F.mul(x, x)), FS.value(one, x)), FO.mul_v(one, h1, F.mul(x, x), x, h2, hx)) : {FS.madd(FS.prime(one), _, FS.value(one, F.small(7n))) == FS.madd(FS.prime(one), FS.mmul(FS.prime(one), FS.mmul(FS.prime(one), FS.value(one, x), FS.value(one, x)), FS.value(one, x)), 7n) : Nat}
  %Equal.sym(Nat, FS.value(one, F.mul(x, x)), FS.mmul(FS.prime(one), FS.value(one, x), FS.value(one, x)), FO.mul_v(one, h1, x, x, hx, hx)) : {FS.madd(FS.prime(one), FS.mmul(FS.prime(one), _, FS.value(one, x)), FS.value(one, F.small(7n))) == FS.madd(FS.prime(one), FS.mmul(FS.prime(one), FS.mmul(FS.prime(one), FS.value(one, x), FS.value(one, x)), FS.value(one, x)), 7n) : Nat}
  %Equal.sym(Nat, FS.value(one, F.small(7n)), 7n, FO.small_val(one, h1, 7n, seven_lt(one, h1))) : {FS.madd(FS.prime(one), FS.mmul(FS.prime(one), FS.mmul(FS.prime(one), FS.value(one, x), FS.value(one, x)), FS.value(one, x)), _) == FS.madd(FS.prime(one), FS.mmul(FS.prime(one), FS.mmul(FS.prime(one), FS.value(one, x), FS.value(one, x)), FS.value(one, x)), 7n) : Nat}
  {==}

Uses (20):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&name=add_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&name=mul_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&name=mul_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&name=small_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&name=small_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/penc.bend&name=seven_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend&name=red
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend&name=rhs
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=madd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=mmul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=prime
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend&name=add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend&name=mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend&name=small
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend&name=rhs