Consts.hm_p: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend as Consts
Lines 113-121 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&start_line=113&end_line=121

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
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/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend as SR

def hm_p(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.add(1n+pp(one), FS.cp(one)) == C.shift(256n, one) : Nat}:
  %Equal.sym(Nat, C.shift(256n, one), Nat.add(Nat.add(FS.cp(one), 1n), pp(one)), Equal.sym(Nat, Nat.add(Nat.add(FS.cp(one), 1n), pp(one)), C.shift(256n, one), pp_sum(one, h1))) : {Nat.add(1n+pp(one), FS.cp(one)) == _ : Nat}
  %Equal.sym(Nat, 1n+pp(one), Nat.add(pp(one), 1n), SR.succ_add(1n, pp(one))) : {Nat.add(_, FS.cp(one)) == Nat.add(Nat.add(FS.cp(one), 1n), pp(one)) : Nat}
  %Equal.sym(Nat, Nat.add(Nat.add(pp(one), 1n), FS.cp(one)), Nat.add(pp(one), Nat.add(1n, FS.cp(one))), NA.add_assoc(pp(one), 1n, FS.cp(one))) : {_ == Nat.add(Nat.add(FS.cp(one), 1n), pp(one)) : Nat}
  %Equal.sym(Nat, Nat.add(1n, FS.cp(one)), Nat.add(FS.cp(one), 1n), NA.add_comm(1n, FS.cp(one))) : {Nat.add(pp(one), _) == Nat.add(Nat.add(FS.cp(one), 1n), pp(one)) : Nat}
  %Equal.sym(Nat, Nat.add(pp(one), Nat.add(FS.cp(one), 1n)), Nat.add(FS.cp(one), Nat.add(pp(one), 1n)), NA.add_swap(pp(one), FS.cp(one), 1n)) : {_ == Nat.add(Nat.add(FS.cp(one), 1n), pp(one)) : Nat}
  %Equal.sym(Nat, Nat.add(Nat.add(FS.cp(one), 1n), pp(one)), Nat.add(FS.cp(one), Nat.add(1n, pp(one))), NA.add_assoc(FS.cp(one), 1n, pp(one))) : {Nat.add(FS.cp(one), Nat.add(pp(one), 1n)) == _ : Nat}
  %Equal.sym(Nat, Nat.add(1n, pp(one)), Nat.add(pp(one), 1n), NA.add_comm(1n, pp(one))) : {Nat.add(FS.cp(one), Nat.add(pp(one), 1n)) == Nat.add(FS.cp(one), _) : Nat}
  {==}

Uses (11):
  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=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=pp
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=pp_sum
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend&name=succ_add
  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
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=cp
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift