PROOFOrder.wd.lt_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 269-276 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=269&end_line=276

import Base

def wd.lt_trans(n: Nat, a: Word(n), b: Word(n), c: Word(n), +h1: {Word.cmp(n, a, b) == LT{} : Cmp}, +h2: {Word.cmp(n, b, c) == LT{} : Cmp}) -> {Word.cmp(n, a, c) == LT{} : Cmp}:
  match n:
    case 0n:
      Empty.absurd({Word.cmp(0n, a, c) == LT{} : Cmp}, ab.eq_lt(h1))
    case 1n+ +p:
      match a b c:
        case WCon{+x, +at} WCon{+y, +bt} WCon{+z, +ct}:
          wd.fin_trans(Word.cmp(p, at, bt), Word.cmp(p, bt, ct), p, x, y, z, at, bt, ct, {==}, {==}, h1, h2, u => w => wd.lt_trans(p, at, bt, ct, u, w))

Uses (8):
  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=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.cmp
  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=wd.fin_trans