Cong.c_pow: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend as Cong
Lines 57-61 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend&start_line=57&end_line=61

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/modpow.bend as MP

def c_pow(+pp: Nat, +a: Nat, +a2: Nat, +k: Nat, +ha: ceq(pp, a, a2)) -> ceq(pp, Nat.pow(a, k), Nat.pow(a2, k)):
  +n = {1n+pp : Nat}
  +e1 = Equal.sym(Nat, Nat.mod(Nat.pow(Nat.mod(a, n), k), n), Nat.mod(Nat.pow(a, k), n), MP.mod_pow(pp, a, k))
  +e2 = Equal.cong(Nat, Nat, t => Nat.mod(Nat.pow(t, k), n), Nat.mod(a, n), Nat.mod(a2, n), ha)
  Equal.trans(Nat, Nat.mod(Nat.pow(a, k), n), Nat.mod(Nat.pow(Nat.mod(a, n), k), n), Nat.mod(Nat.pow(a2, k), n), e1, Equal.trans(Nat, Nat.mod(Nat.pow(Nat.mod(a, n), k), n), Nat.mod(Nat.pow(Nat.mod(a2, n), k), n), Nat.mod(Nat.pow(a2, k), n), e2, MP.mod_pow(pp, a2, k)))

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.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.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/crypto/curve25519/cong.bend&name=ceq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/modpow.bend&name=mod_pow