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Proof step 20 from proof inv-link (previous step)

dent = negdentry(str), err = ESUCCESS, ino = ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px-parent(user, q, ROOT_INO, dirs, files) ⊦ ⟪afs_iget#(ino, dirs, files, asynced; inode, err); if err = ESUCCESS then if ¬ inode.directory then err := ENOTDIR else if ¬ px(user, inode.meta) then err := EACCESS else {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then afs_iget#(dent.ino, dirs, files, asynced; inode, err); if err = ESUCCESS ∧ inode.directory then err := EISDIR}; c_inode := inode; old_dent := dent; if err = ESUCCESS then let ino = ROOT_INO, dent = negdentry(p.last), p0 = parent(p) in {vfs_walk#(p0, user, dirs, files, asynced; ino, err); 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 afs_link#(old_dent; new_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), p = ε

User applied rule insert program lemma

And obtained the following new goals

Proof step 21:
afs-cons(dirs, files), pre-iget(ino, dirs, files) ⊦ ⟪afs_iget#(ino, dirs, files, asynced; inode, err)⟫ true
Proof step 22:
asynced0 ↔ asynced, dent = negdentry(str), dirs0 = dirs, err = ESUCCESS, files0 = files, ino = ino0, ino1 = ino, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pre-iget(ino, dirs, files), px-parent(user, q, ROOT_INO, dirs, files) ⊦ [afs_iget#(ino, dirs, files, asynced; inode, err)] ( true → ⟪if err = ESUCCESS then if ¬ inode.directory then err := ENOTDIR else if ¬ px(user, inode.meta) then err := EACCESS else {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then afs_iget#(dent.ino, dirs, files, asynced; inode, err); if err = ESUCCESS ∧ inode.directory then err := EISDIR}; c_inode := inode; old_dent := dent; if err = ESUCCESS then let ino = ROOT_INO, dent = negdentry(p.last), p0 = parent(p) in {vfs_walk#(p0, user, dirs, files, asynced; ino, err); 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 afs_link#(old_dent; new_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))), p = ε

Rule argument

spec: afs-asm name: inv-iget seq: afs-cons(dirs, files), pre-iget(ino, dirs, files) ⊦ ⟪afs_iget#(ino, dirs, files, asynced; inode, err)⟫ true subst: [asynced, files, dirs, ino, err, inode] → [asynced, files, dirs, ino, err, inode] flags: <all paths>

Additional information

Used simplifier rules: ⊦ pre-iget(ino, dirs, files) ↔ valid-ino(ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%path-in-end: ⊦ ispath(p, n, m, dirs, files) ∧ ¬ m ∈ files → m ∈ dirs; (forward) from specification afs-base