F64bl.hbits: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bl.bend as F64bl
Lines 32-37 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bl.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bl.bend&start_line=32&end_line=37

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA

def hbits(+k: Nat, +n: Nat) -> {F.high_bits(k, n) == C.high(k, n) : Nat}:
  match k:
    case 0n:
      {==}
    case 1n+ +p:
      Equal.trans(Nat, F.high_bits(p, Nat.div(n, 2n)), F.high_bits(p, C.half(n)), C.high(p, C.half(n)), Equal.cong(Nat, Nat, z => F.high_bits(p, z), Nat.div(n, 2n), C.half(n), Equal.sym(Nat, C.half(n), Nat.div(n, 2n), WA.half_div(n))), hbits(p, C.half(n)))

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.div
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend&name=half_div
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=half
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=high
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=high_bits