Modexp.pow0: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/modexp.bend as Modexp
Lines 25-27 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/modexp.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/modexp.bend&start_line=25&end_line=27

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

# x^0 mod m = 1 for m > 1
def pow0(+mp: Nat, +x: Nat, +h: {Nat.is_lt(1n, 1n+mp) == True{} : Bool}) -> {1n == Nat.mod(Nat.pow(x, 0n), 1n+mp) : Nat}:
  Equal.sym(Nat, Nat.mod(1n, 1n+mp), 1n, NR.mod_of(0n, mp, 1n, h))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend&name=mod_of