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Proof step 62 from proof walk-term (previous step)

dirs[ino] = mkdir(m, md, # links(ino, dirs), m1, entries), dent = negdentry(str), err = ENOENT, err0 = ESUCCESS, p = str ' + p1, p_ino = ino, afs-cons(dirs, files), px(user, md), ino ∈ dirs, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, ∀ p0, err, dirs, files, ino, user, asynced. # p0 < #(str + p1) → err = ESUCCESS ∧ afs-cons(dirs, files) ∧ (ino ∈ dirs ∨ ino ∈ files) ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO) → ⟪while p0 ≠ 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(p0.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p0 := p0.tail}}}⟫ true ⊦ ⟪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}}}⟫ true, dent.name ∈ dirs[p_ino].entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 63:
dirs[ino] = mkdir(m, md, # links(ino, dirs), m1, entries), err = ENOENT, p = str ' + p1, afs-cons(dirs, files), px(user, md), ino ∈ dirs, ¬ str ∈ entries, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, ∀ p0, err, dirs, files, ino, user, asynced. # p0 < #(str + p1) → err = ESUCCESS ∧ afs-cons(dirs, files) ∧ (ino ∈ dirs ∨ ino ∈ files) ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO) → ⟪while p0 ≠ 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(p0.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p0 := p0.tail}}}⟫ true ⊦ ⟪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}}}⟫ true

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ str ∈ str0 ' + p ↔ str = str0 ∨ str ∈ p; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]%in-14: ⊦ str ' + p = p0 → str ∈ p0; (forward) from specification list[path]% ⊦ negdentry(str).name = str; (s)