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Proof step 195 from proof refine-create (previous step)

dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m3, entries0), fs = abs-files(files0), # links(ino1, dirs0) ≠ 0, ino1 ≠ ROOT_INO, ino2 ≠ 0, links(ino1, dirs0) ≠ ∅, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino1 ∈ dirs0, dirs ≡ dirs0[ino1, mkdir(# entries0 + 1, md0, # links(ino1, dirs0), m3, entries0[str, ino2])], ¬ str ∈ entries0, ¬ ino2 ∈ files0, ¬ ino2 ∈ dirs0, ¬ ino1 ∈ dirs, ¬ ino2 ∈ dirs, psynced → asynced0 ⊦ ⟨posix_create#(q + str ', md, user, abs-of(of); err2, root, fs; psynced)⟩ (fs = abs-files((files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err2)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 196:
dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m3, entries0), err0 = err2, fs = abs-files(files0), ofh = abs-of(of), path = q + str ', root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino1 ∈ dirs0, dirs ≡ dirs0[ino1, mkdir(# entries0 + 1, md0, # links(ino1, dirs0), m3, entries0[str, ino2])], psynced → asynced0 ⊦ ⟨choose err with pre-create(path, md, err, user, root, fs, ofh) in err0 := err; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files((files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), # links(ino1, dirs0) = 0, ino1 = ROOT_INO, ino2 = 0, links(ino1, dirs0) = ∅, str ∈ entries0, ino2 ∈ files0, ino2 ∈ dirs0, ino1 ∈ dirs, ino2 ∈ dirs

Rule argument

pos: right 1

Additional information

Used simplifier rules: posix_create#(PATH, MD, USER, OFH; ERR, ROOT, FS; PSYNCED) {choose E with pre-create(PATH, MD, E, USER, ROOT, FS, OFH) in ERR := E; if ERR = ESUCCESS then choose FID with ¬ FID ∈ FS in {ROOT[PATH] := fnode(FID); FS[FID] := mkfile(MD, mkbuf(0))}; PSYNCED := ? };