Lemire.dbl_add: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend as Lemire
Lines 240-246 of bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&start_line=240&end_line=246

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

def dbl_add(+z: Nat) -> {Nat.double(z) == Nat.add(z, z) : Nat}:
  match z:
    case 0n:
      {==}
    case 1n+p:
      %Equal.sym(Nat, Nat.add(p, 1n+p), 1n+Nat.add(p, p), N.add_succ(p, p)) : {2n+Nat.double(p) == 1n+_ : Nat}
      Equal.cong(Nat, Nat, x => 2n+x, Nat.double(p), Nat.add(p, p), dbl_add(p))

Uses (6):
  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=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-math@1.0.0.0/proofs/lib/nat.bend&name=add_succ