Rel.rc_add: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/rel.bend as Rel
Lines 25-27 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/rel.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/rel.bend&start_line=25&end_line=27

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend as FO
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend as G

def rc_add(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +x: List<&2, U32>, +y: List<&2, U32>, +a: Nat, +b: Nat, +ox: {LM.okb(32n, x, 255n) == True{} : Bool}, +cx: G.ceq(pp, FS.value(x), a), +oy: {LM.okb(32n, y, 255n) == True{} : Bool}, +cy: G.ceq(pp, FS.value(y), b)) -> G.ceq(pp, FS.value(F.add(x, y)), FS.fadd(1n+pp, a, b)):
  +e = G.c_trans(pp, FS.value(F.add(x, y)), Nat.add(FS.value(x), FS.value(y)), FS.fadd(1n+pp, a, b), FO.add_mod(one, h1, pp, hP, x, y, ox, oy), G.c_trans(pp, Nat.add(FS.value(x), FS.value(y)), Nat.add(a, b), FS.fadd(1n+pp, a, b), G.c_add(pp, FS.value(x), a, FS.value(y), b, cx, cy), G.c_sym(pp, Nat.mod(Nat.add(a, b), 1n+pp), Nat.add(a, b), G.c_mod(pp, Nat.add(a, b)))))
  e

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend&name=c_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend&name=c_mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend&name=c_sym
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend&name=c_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend&name=ceq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend&name=add_mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=okb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend&name=fadd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=add