Scalarops.add_v: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend as Scalarops
Lines 93-99 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend&start_line=93&end_line=99

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/src/crypto/secp256k1/scalar.bend as S
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fprot.bend as FR

def add_v(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, Nat>, +b: List<&2, Nat>, +ha: {FS.reduced(one, FS.order(one), a) == True{} : Bool}, +hb: {FS.reduced(one, FS.order(one), b) == True{} : Bool}) -> {FS.value(one, S.add(a, b)) == FS.madd(FS.order(one), FS.value(one, a), FS.value(one, b)) : Nat}:
  %Equal.sym(List<&2, Nat>, S.add(a, b), S.add_u(a, b), FR.s_add(a, b)) : {FS.value(one, _) == FS.madd(FS.order(one), FS.value(one, a), FS.value(one, b)) : Nat}
  %Equal.sym(Nat, FS.value(one, S.reduce_u(L.add(a, b))), Nat.mod(LV.ev(L.add(a, b)), FS.order(one)), red_v(one, h1, L.add(a, b), add_hx(one, h1, a, b, ha, hb))) : {_ == Nat.mod(Nat.add(FS.value(one, a), FS.value(one, b)), FS.order(one)) : Nat}
  %Equal.sym(Nat, LV.ev(L.add(a, b)), Nat.add(LV.ev(a), LV.ev(b)), LV.add_v(a, b)) : {Nat.mod(_, FS.order(one)) == Nat.mod(Nat.add(FS.value(one, a), FS.value(one, b)), FS.order(one)) : Nat}
  %Equal.sym(Nat, LV.ev(a), FS.value(one, a), Equal.sym(Nat, FS.value(one, a), LV.ev(a), LV.ev_value(one, h1, a))) : {Nat.mod(Nat.add(_, LV.ev(b)), FS.order(one)) == Nat.mod(Nat.add(FS.value(one, a), FS.value(one, b)), FS.order(one)) : Nat}
  %Equal.sym(Nat, LV.ev(b), FS.value(one, b), Equal.sym(Nat, FS.value(one, b), LV.ev(b), LV.ev_value(one, h1, b))) : {Nat.mod(Nat.add(FS.value(one, a), _), FS.order(one)) == Nat.mod(Nat.add(FS.value(one, a), FS.value(one, b)), FS.order(one)) : 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=Base/base.bend&name=Nat.add
  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/fprot.bend&name=s_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=add_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=ev
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=ev_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend&name=add_hx
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend&name=red_v
  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=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/limbs.bend&name=add
  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=add_u
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/scalar.bend&name=reduce_u