Fieldops.add_r: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend as Fieldops
Lines 101-103 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&start_line=101&end_line=103

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/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fprot.bend as FR

def add_r(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, Nat>, +b: List<&2, Nat>, +ha: {FS.reduced(one, FS.prime(one), a) == True{} : Bool}, +hb: {FS.reduced(one, FS.prime(one), b) == True{} : Bool}) -> {FS.reduced(one, FS.prime(one), F.add(a, b)) == True{} : Bool}:
  %Equal.sym(List<&2, Nat>, F.add(a, b), F.add_u(a, b), FR.f_add(a, b)) : {FS.reduced(one, FS.prime(one), _) == True{} : Bool}
  red_r(one, h1, L.add(a, b), add_hx(one, h1, a, b, ha, hb))

Uses (12):
  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_hx
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&name=red_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fprot.bend&name=f_add
  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=reduced
  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=add_u
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=add