Bitsv.two_x: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsv.bend as Bitsv
Lines 63-67 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsv.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsv.bend&start_line=63&end_line=67

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

# d < 2 s gives d / 2 < s
def two_x(+x: Nat) -> {Nat.mul(x, 2n) == Nat.add(x, x) : Nat}:
  %Equal.sym(Nat, Nat.mul(x, 2n), Nat.mul(2n, x), NA.mul_comm(x, 2n)) : {_ == Nat.add(x, x) : Nat}
  %Equal.sym(Nat, Nat.add(x, 0n), x, NA.add_zero(x)) : {Nat.add(x, _) == Nat.add(x, x) : Nat}
  {==}

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