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Proof step 84 from proof inv-link (previous step)

dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), c_inode = inode, dent = negdentry(p.last), err = ESUCCESS, err0 = ESUCCESS, ino = ROOT_INO, ino1 = mkdentry(str, entries0[str]).ino, inode = getinode(ino1, dirs, files), inode0 = mkinode(ino0, md0, true, # links(ino0, dirs), m3, m0), p0 = parent(p), mkdentry(str, entries0[str]).dentry?, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pre-iget(ino1, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino0 ∈ dirs, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪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#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), p = ε, err = ESUCCESS ∧ inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 85:
dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), err = ESUCCESS, ino = ROOT_INO, p ≠ ε, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino0 ∈ dirs, entries0[str] ∈ files, ¬ entries0[str] ∈ dirs, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪vfs_walk#(parent(p), user, dirs, files, asynced; ino, err); inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); dent := negdentry(p.last); 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 {c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err, dirs, files; asynced)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ pre-iget(ino, dirs, files) ↔ valid-ino(ino, dirs, files); (s)% ⊦ mkdentry(str, m).ino = m; (s)