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Proof step 16 from proof refine-create (previous step)

fs = abs-files(files), path = ε, root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ ispath(path, ROOT_INO, dirs, files) ∧ ⟨err0 := EEXISTS; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EEXISTS = err0)

Heuristic dl case distinction applied rule case distinction

And obtained the following new goals

Proof step 17:
fs = abs-files(files), path = ε, root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ ⟨err0 := EEXISTS; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EEXISTS = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ ispath(ε, n, dirs, files) ↔ n ∈ dirs ∨ n ∈ files; (s)% ⊦ afs-cons(dirs, files) → ROOT_INO ∈ dirs; (ss)