U32half.hlf_lt: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32half.bend as U32half
Lines 124-135 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32half.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32half.bend&start_line=124&end_line=135

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

# s < 2m gives s/2 < m: one narrowing step of a search range that started
# below 2^f lands below 2^(f-1).
def hlf_lt(+s: Nat, +m: Nat, +h: {Nat.is_lt(s, Nat.double(m)) == True{} : Bool}) -> {Nat.is_lt(hlf(s), m) == True{} : Bool}:
  match s m:
    case s0 0n:
      Empty.absurd({Nat.is_lt(hlf(s0), 0n) == True{} : Bool}, N.lt_zero_absurd(s0, h))
    case 0n 1n+q:
      {==}
    case 1n+0n 1n+q:
      {==}
    case 1n+1n+r 1n+q:
      hlf_lt(r, q, h)

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32half.bend&name=hlf