Width.hb: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as Width
Lines 45-53 of bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend&start_line=45&end_line=53

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

def hb(+n: Nat) -> {n == Nat.add(C.bit(n), Nat.double(C.half(n))) : Nat}:
  match n:
    case 0n:
      {==}
    case 1n:
      {==}
    case 2n+ +q:
      +e = hb(q)
      Equal.trans(Nat, 2n+q, 2n+Nat.add(C.bit(q), Nat.double(C.half(q))), Nat.add(C.bit(q), 2n+Nat.double(C.half(q))), Equal.cong(Nat, Nat, t => 2n+t, q, Nat.add(C.bit(q), Nat.double(C.half(q))), e), Equal.sym(Nat, Nat.add(C.bit(q), 2n+Nat.double(C.half(q))), 2n+Nat.add(C.bit(q), Nat.double(C.half(q))), Equal.trans(Nat, Nat.add(C.bit(q), 2n+Nat.double(C.half(q))), 1n+Nat.add(C.bit(q), 1n+Nat.double(C.half(q))), 2n+Nat.add(C.bit(q), Nat.double(C.half(q))), NA.add_succ(C.bit(q), 1n+Nat.double(C.half(q))), Equal.cong(Nat, Nat, t => 1n+t, Nat.add(C.bit(q), 1n+Nat.double(C.half(q))), 1n+Nat.add(C.bit(q), Nat.double(C.half(q))), NA.add_succ(C.bit(q), Nat.double(C.half(q)))))))

Uses (9):
  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.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=add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=bit
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=half