Num.sc_dbl: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as Num
Lines 47-49 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend&start_line=47&end_line=49

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

# 2^k x + 2^k x == 2^(k+1) x
def sc_dbl(+k: Nat, +x: Nat) -> {Nat.add(WD.sc(k, x), WD.sc(k, x)) == WD.sc(1n+k, x) : Nat}:
  Equal.sym(Nat, Nat.double(WD.sc(k, x)), Nat.add(WD.sc(k, x), WD.sc(k, x)), NA.double_self(WD.sc(k, x)))

Uses (6):
  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=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=double_self
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc