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Proof step 33 from proof walk-term (previous step)

err = EACCESS, p ≠ ε, afs-cons(dirs, files), ino ∈ dirs, ¬ px(user, dirs[ino].meta), links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, ∀ p0, err, dirs, files, ino, user, asynced. # p0 < # p → 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 34:
dirs[ino] = mkdir(m, md, m0, m1, entries), err = EACCESS, afs-cons(dirs, files), ino ∈ dirs, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, ∀ p0, err, dirs, files, ino, user, asynced. # p0 < # p → 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, p = ε, px(user, md)

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[ino], m, md, m0, m1, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[ino], m, md, m0, m1, entries