def wd.lt_trans
bend-osdev-u32@0.1.0.0 · PROOF_order.bend:269
import bend-osdev-u32@0.1.0.0/PROOF_order.bend as PROOFOrder
import Base
269def 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}:
270 match n:
271 case 0n:
272 Empty.absurd({Word.cmp(0n, a, c) == LT{} : Cmp}, ab.eq_lt(h1))
273 case 1n+ +p:
274 match a b c:
275 case WCon{+x, +at} WCon{+y, +bt} WCon{+z, +ct}:
276 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))