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Proof step 194 from proof refine-mkdir (previous step)

dirs0[ino1] = mkdir(# entries0, md1, # links(ino1, dirs0), m1, entries0), # links(ino1, dirs0) ≠ 0, ino1 ≠ ROOT_INO, links(ino1, dirs0) ≠ ∅, ((ino2 => mkdir(0, md, 1, 0, ∅) * (λ dirs1. dirs3 = dirs1)))(dirs), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), of-cons(of, dirs, files), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files), ino2 ∈ dirs4, ino1 ∈ dirs0, dirs ≡ dirs4[ino2, mkdir(0, md, 1, 0, ∅)], dirs4 ≡ dirs3 ++ ino2, dirs3 ≡ dirs0[ino1, mkdir(# entries0 + 1, md1, # links(ino1, dirs0), m1 + 1, entries0[str, ino2])], ¬ ino2 ∈ dirs0, ¬ ino2 ∈ files, ¬ str ∈ entries0, ¬ ino1 ∈ dirs, ¬ ino2 ∈ dirs3, psynced → asynced0 ⊦ ⟨posix_mkdir#(q + str ', md, user, abs-files(files), abs-of(of); err2, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err2)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 195:
dirs0[ino1] = mkdir(# entries0, md1, # links(ino1, dirs0), m1, entries0), err0 = err2, fs = abs-files(files), ofh = abs-of(of), path = q + str ', ((ino2 => mkdir(0, md, 1, 0, ∅) * (λ dirs1. dirs3 = dirs1)))(dirs), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs, files), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs, files), of-cons(of, dirs0, files), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files), ino1 ∈ dirs0, ino2 ∈ dirs4, dirs3 ≡ dirs0[ino1, mkdir(# entries0 + 1, md1, # links(ino1, dirs0), m1 + 1, entries0[str, ino2])], dirs4 ≡ dirs3 ++ ino2, dirs ≡ dirs4[ino2, mkdir(0, md, 1, 0, ∅)], psynced → asynced0 ⊦ ⟨choose err with pre-mkdir(path, md, err, user, root, fs, ofh) in err0 := err; if err0 = ESUCCESS then root[path] := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), # links(ino1, dirs0) = 0, ino1 = ROOT_INO, links(ino1, dirs0) = ∅, ino2 ∈ dirs0, ino2 ∈ files, str ∈ entries0, ino1 ∈ dirs, ino2 ∈ dirs3

Rule argument

pos: right 1

Additional information

Used simplifier rules: posix_mkdir#(PATH, MD, USER, FS, OFH; ERR, ROOT; PSYNCED) {choose E with pre-mkdir(PATH, MD, E, USER, ROOT, FS, OFH) in ERR := E; if ERR = ESUCCESS then ROOT[PATH] := dnode(MD, ∅); PSYNCED := ? };