U32half.step_bound: 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 137-139 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=137&end_line=139

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

# The size after one step is at most s/2, so it stays below the halved bound.
def step_bound(+s2: Nat, +s: Nat, +m: Nat, +hle: {Nat.is_le(s2, hlf(s)) == True{} : Bool}, +h: {Nat.is_lt(s, Nat.double(m)) == True{} : Bool}) -> {Nat.is_lt(s2, m) == True{} : Bool}:
  N.le_lt_trans(s2, hlf(s), m, hle, hlf_lt(s, m, h))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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_le
  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=le_lt_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32half.bend&name=hlf
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32half.bend&name=hlf_lt