Psign.s0_v: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend as Psign
Lines 102-110 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend&start_line=102&end_line=110

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/scalar.bend as S
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend as SO
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarpow.bend as SP
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pscal.bend as SQ

def s0_v(+one: Nat, +h1: {one == 1n : Nat}, +z: List<&2, Nat>, +hz: {FS.reduced(one, FS.order(one), z) == True{} : Bool}, +d: List<&2, Nat>, +hd: {FS.reduced(one, FS.order(one), d) == True{} : Bool}, +k: List<&2, Nat>, +hk: {FS.reduced(one, FS.order(one), k) == True{} : Bool}, +x: List<&2, Nat>, +hx: {FS.limbs16(one, 16n, x) == True{} : Bool}) -> {FS.value(one, S.mul(S.inv(k), S.add(z, S.mul(S.reduce(x), d)))) == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}:
  +hr = SQ.sred_r(one, h1, x, hx)
  +hm = SO.mul_r(one, h1, S.reduce(x), d, hr, hd)
  %Equal.sym(Nat, FS.value(one, S.mul(S.inv(k), S.add(z, S.mul(S.reduce(x), d)))), FS.mmul(FS.order(one), FS.value(one, S.inv(k)), FS.value(one, S.add(z, S.mul(S.reduce(x), d)))), SO.mul_v(one, h1, S.inv(k), S.add(z, S.mul(S.reduce(x), d)), SP.inv_r(one, h1, k, hk), SO.add_r(one, h1, z, S.mul(S.reduce(x), d), hz, hm))) : {_ == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}
  %Equal.sym(Nat, FS.value(one, S.inv(k)), FS.minv(FS.order(one), FS.value(one, k)), SP.inv_v(one, h1, k, hk)) : {FS.mmul(FS.order(one), _, FS.value(one, S.add(z, S.mul(S.reduce(x), d)))) == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}
  %Equal.sym(Nat, FS.value(one, S.add(z, S.mul(S.reduce(x), d))), FS.madd(FS.order(one), FS.value(one, z), FS.value(one, S.mul(S.reduce(x), d))), SO.add_v(one, h1, z, S.mul(S.reduce(x), d), hz, hm)) : {FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), _) == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}
  %Equal.sym(Nat, FS.value(one, S.mul(S.reduce(x), d)), FS.mmul(FS.order(one), FS.value(one, S.reduce(x)), FS.value(one, d)), SO.mul_v(one, h1, S.reduce(x), d, hr, hd)) : {FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), _)) == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}
  %Equal.sym(Nat, FS.value(one, S.reduce(x)), Nat.mod(FS.value(one, x), FS.order(one)), SQ.sred_v(one, h1, x, hx)) : {FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), _, FS.value(one, d)))) == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}
  {==}

Uses (24):
  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=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pscal.bend&name=sred_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pscal.bend&name=sred_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend&name=add_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend&name=add_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend&name=mul_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend&name=mul_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarpow.bend&name=inv_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarpow.bend&name=inv_v
  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/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=minv
  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=order
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=reduced
  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/scalar.bend&name=add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/scalar.bend&name=inv
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/scalar.bend&name=mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/scalar.bend&name=reduce