Rconst.rn_sum: 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 114-118 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=114&end_line=118

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as NR

# with P + c_p = N + c_n and c_n <= r + P: (r + P - c_n) + c_p = r + N
def rn_sum(+r: Nat, +nn: Nat, +pp: Nat, +cn: Nat, +cp: Nat, +hs: {Nat.add(1n+pp, cp) == Nat.add(nn, cn) : Nat}, +hl: {Nat.is_le(cn, Nat.add(r, 1n+pp)) == True{} : Bool}) -> {Nat.add(Nat.sub(Nat.add(r, 1n+pp), cn), cp) == Nat.add(r, nn) : Nat}:
  +d = Nat.sub(Nat.add(r, 1n+pp), cn)
  +sa = N.sub_add(Nat.add(r, 1n+pp), cn, hl)
  NR.add_cancel(cn, Nat.add(d, cp), Nat.add(r, nn), rn_sum_c(r, nn, pp, cn, cp, hs, sa))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.is_le
  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/crypto/secp256k1/rconst.bend&name=rn_sum_c
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=sub_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend&name=add_cancel