ProofTab.gt.fl_split: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/proof_tab.bend as ProofTab
Lines 296-303 of bend-osdev-gf@0.1.1.0/proof_tab.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&start_line=296&end_line=303

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

# the log fill splits: n + m writes are n writes, then m more
def 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>}:
  match n:
    case 0n:
      {==}
    case 1n+j:
      %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>}
      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)

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.set
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.index
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8.exp
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Field
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.fl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_succ