Pow.pow_one_one: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend as Pow
Lines 139-142 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend&start_line=139&end_line=142

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

# a^one * 1 == a
def pow_one_one(+one: Nat, +h1: {one == 1n : Nat}, +a: Nat) -> {Nat.mul(Nat.pow(a, one), 1n) == a : Nat}:
  +e = L.subst(Nat, o => {Nat.pow(a, o) == a : Nat}, 1n, one, Equal.sym(Nat, one, 1n, h1), NA.mul_one(a))
  Equal.trans(Nat, Nat.mul(Nat.pow(a, one), 1n), Nat.pow(a, one), a, NA.mul_one(Nat.pow(a, one)), e)

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=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.mul
  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/lib/lemmas/proofs/nat_algebra.bend&name=mul_one
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst