PROOFOrder.wd.bool_trans: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF_order.bend as PROOFOrder
Lines 234-245 of bend-osdev-u32@0.1.0.0/PROOF_order.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF_order.bend&start_line=234&end_line=245

import Base

def wd.bool_trans(x: Bool, y: Bool, z: Bool, +h1: {Bool.cmp(x, y) == LT{} : Cmp}, +h2: {Bool.cmp(y, z) == LT{} : Cmp}) -> {Bool.cmp(x, z) == LT{} : Cmp}:
  match x y z:
    case False{} False{} z:
      Empty.absurd({Bool.cmp(False{}, z) == LT{} : Cmp}, ab.eq_lt(h1))
    case False{} True{} False{}:
      Empty.absurd({EQ{} == LT{} : Cmp}, ab.gt_lt(h2))
    case False{} True{} True{}:
      Empty.absurd({LT{} == LT{} : Cmp}, ab.eq_lt(h2))
    case True{} False{} z:
      Empty.absurd({Bool.cmp(True{}, z) == LT{} : Cmp}, ab.gt_lt(h1))
    case True{} True{} z:
      Empty.absurd({Bool.cmp(True{}, z) == LT{} : Cmp}, ab.eq_lt(h1))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF_order.bend&name=ab.eq_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF_order.bend&name=ab.gt_lt