def gt.fl_split

bend-osdev-gf@0.1.1.0 · proof_tab.bend:296

import Base
import bend-osdev-array@0.1.0.1/array.bend as A
import bend-osdev-gf@0.1.1.0/gf.bend as G
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

296# the log fill splits: n + m writes are n writes, then m more
297def gt.fl_split(+n: Nat, +m: Nat, xs: List<&2, U32>, +f: G.Gf8Field, +k: Nat) -> {gt.fl(Nat.add(n, m), xs, f, k) == gt.fl(m, gt.fl(n, xs, f, k), f, Nat.add(n, k)) : List<&2, U32>}:
298  match n:
299    case 0n:
300      {==}
301    case 1n+j:
302      %UL.nat_add_succ(j, k) : {gt.fl(Nat.add(j, m), List.set(&2, U32, xs, A.Arrays.index(8n, G.Gf8.exp(f, k)), U32.from_nat(k)), f, 1n+k) == gt.fl(m, gt.fl(j, List.set(&2, U32, xs, A.Arrays.index(8n, G.Gf8.exp(f, k)), U32.from_nat(k)), f, 1n+k), f, _) : List<&2, U32>}
303      gt.fl_split(j, m, List.set(&2, U32, xs, A.Arrays.index(8n, G.Gf8.exp(f, k)), U32.from_nat(k)), f, 1n+k)