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Proof step 88 from proof inv-link (previous step)

asynced0 ↔ asynced, dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), dirs0 = dirs, err = ESUCCESS, files0 = files, ino = ROOT_INO, p0 = parent(p), user0 = user, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino0 ∈ dirs, entries0[str] ∈ files, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ∀ ino, err. ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p0, ROOT_INO, ino, dirs0, files0) ∧ px-parent(user0, p0, ROOT_INO, dirs0, files0) ∨ err = ENOENT ∧ ¬ ispath(p0, ROOT_INO, dirs0, files0) ∨ err = EACCESS ∧ p0 ≠ ε ∧ (∃ p'. p' ⊑ parent(p0) ∧ ispath(p', ROOT_INO, dirs0, files0) ∧ ¬ px(user0, p', ROOT_INO, dirs0, files0)) → ⟪inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); dent := negdentry(p.last); if err = ESUCCESS then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err); new_inode := inode, new_dent := dent; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err, dirs, files; asynced)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), p = ε, entries0[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 89:
dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), p ≠ ε, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ files, ino0 ∈ dirs, str ∈ entries0, ¬ entries0[str] ∈ dirs, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, ⌊err0⌋ ∨ err0 = ESUCCESS ∧ ispath(parent(p), ROOT_INO, ino1, dirs, files) ∧ px-parent(user, parent(p), ROOT_INO, dirs, files) ∨ err0 = ENOENT ∧ ¬ ispath(parent(p), ROOT_INO, dirs, files) ∨ err0 = EACCESS ∧ p ≠ p.head ' ∧ p' ⊑ parent(parent(p)) ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ⊦ ⟪inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); dent := negdentry(p.last); if err0 = ESUCCESS then vfs_may_create#(ino1, dent, user, dirs, files, asynced; inode, err0); new_inode := inode, new_dent := dent; if err0 = ESUCCESS then afs_check_commit#(dirs, files; err0; asynced); if err0 = ESUCCESS then {c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err0, dirs, files; asynced)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ p ≠ ε → (parent(p) = ε ↔ p = p.head '); (s)