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Proof step 40 from proof inv-create (previous step)

dirs[ino0] = mkdir(m, md0, # links(ino0, dirs), m1, entries), dent = negdentry(str), err = ESUCCESS, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs ⊦ ⟪afs_lookup#(ino0, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {dent := negdentry((q + str ').last); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, md0, true, # links(ino0, dirs), m1, m) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ); afs_create#(md; inode, c_inode, dent, err, dirs, files; asynced)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

User applied rule insert program lemma

And obtained the following new goals

Proof step 41:
afs-cons(dirs, files), pre-lookup(p_ino, dent, dirs, files) ⊦ ⟪afs_lookup#(p_ino, dirs, files, asynced; dent, err)⟫ true
Proof step 42:
asynced0 ↔ asynced, dirs[ino0] = mkdir(m, md0, # links(ino0, dirs), m1, entries), dent = negdentry(str), dirs0 = dirs, err = ESUCCESS, files0 = files, p_ino0 = ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pre-lookup(ino0, dent, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs ⊦ [afs_lookup#(ino0, dirs, files, asynced; dent, err)] ( true → ⟪if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {dent := negdentry((q + str ').last); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, md0, true, # links(ino0, dirs), m1, m) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ); afs_create#(md; inode, c_inode, dent, err, dirs, files; asynced)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)))

Rule argument

spec: afs-asm name: inv-lookup seq: afs-cons(dirs, files), pre-lookup(p_ino, dent, dirs, files) ⊦ ⟪afs_lookup#(p_ino, dirs, files, asynced; dent, err)⟫ true subst: [asynced, files, dirs, p_ino, err, dent] → [asynced, files, dirs, ino0, err, dent] flags: <all paths>

Additional information

Used simplifier rules: ⊦ pre-lookup(p_ino, dent, dirs, files) ↔ valid-parent-ino(p_ino, dirs, files); (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)%⊦ ispath(p, ino, n, dirs, files) → (# links(n, dirs) = 0 ↔ p = ε ∧ links(ino, dirs) = ∅); (ws)% ⊦ afs-cons(dirs, files) → ROOT_INO ∈ dirs; (ss)% ⊦ afs-cons(dirs, files) → ¬ ROOT_INO ∈ files; (s)% ⊦ px-parent(user, ε, ino, dirs, files); (s)% ⊦ ispath(ε, n, m, dirs, files) ↔ valid-ino(n, dirs, files) ∧ m = n; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)