Rconst.rn_sum_c: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/rconst.bend as Rconst
Lines 103-112 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/rconst.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/rconst.bend&start_line=103&end_line=112

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

def rn_sum_c(+r: Nat, +nn: Nat, +pp: Nat, +cn: Nat, +cp: Nat, +hs: {Nat.add(1n+pp, cp) == Nat.add(nn, cn) : Nat}, +sa: {Nat.add(cn, Nat.sub(Nat.add(r, 1n+pp), cn)) == Nat.add(r, 1n+pp) : Nat}) -> {Nat.add(cn, Nat.add(Nat.sub(Nat.add(r, 1n+pp), cn), cp)) == Nat.add(cn, Nat.add(r, nn)) : Nat}:
  %Equal.sym(Nat, Nat.add(cn, Nat.add(Nat.sub(Nat.add(r, 1n+pp), cn), cp)), Nat.add(Nat.add(cn, Nat.sub(Nat.add(r, 1n+pp), cn)), cp), Equal.sym(Nat, Nat.add(Nat.add(cn, Nat.sub(Nat.add(r, 1n+pp), cn)), cp), Nat.add(cn, Nat.add(Nat.sub(Nat.add(r, 1n+pp), cn), cp)), NA.add_assoc(cn, Nat.sub(Nat.add(r, 1n+pp), cn), cp))) : {_ == Nat.add(cn, Nat.add(r, nn)) : Nat}
  %Equal.sym(Nat, Nat.add(cn, Nat.sub(Nat.add(r, 1n+pp), cn)), Nat.add(r, 1n+pp), sa) : {Nat.add(_, cp) == Nat.add(cn, Nat.add(r, nn)) : Nat}
  %Equal.sym(Nat, Nat.add(Nat.add(r, 1n+pp), cp), Nat.add(r, Nat.add(1n+pp, cp)), NA.add_assoc(r, 1n+pp, cp)) : {_ == Nat.add(cn, Nat.add(r, nn)) : Nat}
  %Equal.sym(Nat, Nat.add(1n+pp, cp), Nat.add(nn, cn), hs) : {Nat.add(r, _) == Nat.add(cn, Nat.add(r, nn)) : Nat}
  %Equal.sym(Nat, Nat.add(nn, cn), Nat.add(cn, nn), NA.add_comm(nn, cn)) : {Nat.add(r, _) == Nat.add(cn, Nat.add(r, nn)) : Nat}
  %Equal.sym(Nat, Nat.add(r, Nat.add(cn, nn)), Nat.add(cn, Nat.add(r, nn)), NA.add_swap(r, cn, nn)) : {_ == Nat.add(cn, Nat.add(r, nn)) : Nat}
  %Equal.sym(Nat, Nat.add(r, nn), Nat.add(nn, r), NA.add_comm(r, nn)) : {Nat.add(cn, _) == Nat.add(cn, Nat.add(r, nn)) : Nat}
  %Equal.sym(Nat, Nat.add(r, nn), Nat.add(nn, r), NA.add_comm(r, nn)) : {Nat.add(cn, Nat.add(nn, r)) == Nat.add(cn, _) : Nat}
  {==}

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_swap