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Proof step 111 from proof walk-prepost-h (previous step)

dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), dent = negdentry(str0), err = ESUCCESS, p2 = str0 + p0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), px(user, dirs[entries0[str]].meta), px(user, md0), entries0[str] ∈ dirs, str ∈ entries0, ino0 ∈ dirs, q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files), links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, ∀ p1, err, p, p_ino, ino, dirs, files, q, user, asynced. # p1 < #(str + p2) → err = ESUCCESS ∧ p = p1 ∧ p_ino = ino ∧ afs-cons(dirs, files) ∧ ispath(q, ROOT_INO, ino, dirs, files) ∧ ino ∈ dirs ∧ (q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files)) → [while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p1, p_ino, ino, dirs, files) ∧ px-parent(user, q + p1, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p1, p_ino, dirs, files) ∨ err = EACCESS ∧ p1 ≠ ε ∧ (∃ p'. p' ⊑ parent(p1) ∧ ispath(p', p_ino, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))) ⊦ [afs_lookup#(entries0[str], dirs, files, asynced; dent, err); p := p2; ino := entries0[str]; if err = ESUCCESS then {ino := dent.ino; p := p.tail}; while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p2, entries0[str], ino, dirs, files) ∧ px-parent(user, q + str ' + p2, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p2, entries0[str], dirs, files) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ str ' + parent(p2) ∧ ispath(p', ino0, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))), p2 = ε, ispath(q + str ', ROOT_INO, entries0[str], dirs, files) ∧ px(user, q, ROOT_INO, dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 112:
dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), dent = negdentry(str0), err = ESUCCESS, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), px(user, md0), px(user, dirs[entries0[str]].meta), ino0 ∈ dirs, str ∈ entries0, entries0[str] ∈ dirs, q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files), links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, ∀ p1, err, p, p_ino, ino, dirs, files, q, user, asynced. # p1 < #(str + str0 + p0) → err = ESUCCESS ∧ p = p1 ∧ p_ino = ino ∧ afs-cons(dirs, files) ∧ ispath(q, ROOT_INO, ino, dirs, files) ∧ ino ∈ dirs ∧ (q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files)) → [while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p1, p_ino, ino, dirs, files) ∧ px-parent(user, q + p1, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p1, p_ino, dirs, files) ∨ err = EACCESS ∧ p1 ≠ ε ∧ (∃ p'. p' ⊑ parent(p1) ∧ ispath(p', p_ino, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))) ⊦ [afs_lookup#(entries0[str], dirs, files, asynced; dent, err); p := str0 ' + p0; ino := entries0[str]; if err = ESUCCESS then {ino := dent.ino; p := p.tail}; while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}] ( ⌊err⌋ ∨ err = ESUCCESS ∧ str0 ∈ dirs[entries0[str]].entries ∧ ispath(p0, dirs[entries0[str]].entries[str0], ino, dirs, files) ∧ px-parent(user, q + str ' + str0 ' + p0, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ (¬ str0 ∈ dirs[entries0[str]].entries ∨ ¬ ispath(p0, dirs[entries0[str]].entries[str0], dirs, files)) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ str ' + parent(str0 ' + p0) ∧ ispath(p', ino0, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files))), ispath(q + str ', ROOT_INO, entries0[str], dirs, files) ∧ px(user, q, ROOT_INO, dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ ispath(str ' + q, n, dirs, files) ↔ valid-dir-ino(n, dirs, files) ∧ str ∈ dirs[n].entries ∧ ispath(q, dirs[n].entries[str], dirs, files); (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ ispath(str ' + p, n, m, dirs, files) ↔ valid-dir-ino(n, dirs, files) ∧ str ∈ dirs[n].entries ∧ ispath(p, dirs[n].entries[str], m, dirs, files); (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ str ' + p ≠ ε; (s)% ⊦ str + p = str ' + p; (s)