PROOF.un.lt_half: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 2092-2097 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=2092&end_line=2097

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U

def un.lt_half(y: Bool, +v: Nat, +d: Nat, h: {Nat.is_lt(Nat.add(U.U32Nat.bit(y), Nat.double(v)), Nat.double(d)) == True{} : Bool}) -> {Nat.is_lt(v, d) == True{} : Bool}:
  match y:
    case False{}:
      Equal.trans(Bool, Nat.is_lt(v, d), Nat.is_lt(Nat.double(v), Nat.double(d)), True{}, Equal.sym(Bool, Nat.is_lt(Nat.double(v), Nat.double(d)), Nat.is_lt(v, d), un.lt_dbl(v, d)), h)
    case True{}:
      Equal.trans(Bool, Nat.is_lt(v, d), Nat.is_lt(1n+Nat.double(v), Nat.double(d)), True{}, Equal.sym(Bool, Nat.is_lt(1n+Nat.double(v), Nat.double(d)), Nat.is_lt(v, d), un.lt_dbl1(v, d)), h)

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.lt_dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.lt_dbl1
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.bit