Prime.hP: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/prime.bend as Prime
Lines 24-27 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/prime.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/prime.bend&start_line=24&end_line=27

import Base
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/lib/lemmas/proofs/nat_algebra.bend as NA

def hP(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.add(1n+pp_of(one), 19n) == WD.sc(255n, one) : Nat}:
  +pp = pp_of(one)
  +e = Equal.cong(Nat, Nat, t => 1n+t, Nat.add(pp, 19n), Nat.add(19n, pp), NA.add_comm(pp, 19n))
  Equal.trans(Nat, Nat.add(1n+pp, 19n), Nat.add(20n, pp), WD.sc(255n, one), e, pp_sum(one, h1))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/prime.bend&name=pp_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/prime.bend&name=pp_sum
  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/word.bend&name=sc