Nat.double_succ: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 517-520 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&start_line=517&end_line=520

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

def double_succ(+y: Nat) -> {Nat.double(1n+y) == Nat.add(2n, Nat.double(y)) : Nat}:
  %Equal.sym(Nat, Nat.double(y), Nat.add(y, y), NA.double_self(y)) : {Nat.double(1n+y) == Nat.add(2n, _) : Nat}
  %Equal.sym(Nat, Nat.double(1n+y), Nat.add(1n+y, 1n+y), NA.double_self(1n+y)) : {_ == Nat.add(2n, Nat.add(y, y)) : Nat}
  succ_cong(Nat.add(y, 1n+y), 1n+Nat.add(y, y), add_succ(y, y))

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=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/nat.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=succ_cong