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Proof step 166 from proof inv-link (previous step)

dirs[ino1] = mkdir(m, md, # links(ino1, dirs), m4, entries1), files[entries[str]] = mkfile(m1, md2, # links(entries[str], dirs), content0), dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), entries0[str] = entries[str], dirs[ino] = mkdir(m2, md1, # links(ino, dirs), m6, entries), c_inode = mkinode(entries[str], md2, false, # links(entries[str], dirs), 0, m1), err0 = ESUCCESS, new_dent = negdentry(p.last), new_inode = mkinode(ino1, md, true, # links(ino1, dirs), m4, m), p ≠ ε, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), ispath(parent(p), ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md0), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, parent(p), ROOT_INO, dirs, files), str ∈ entries0, entries[str] ∈ files, ino0 ∈ dirs, ino1 ∈ dirs, ino ∈ dirs, str ∈ entries, ¬ entries[str] ∈ dirs, ¬ p.last ∈ entries1, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ [afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err0, dirs, files; asynced)] (afs-cons(dirs, files) → of-cons(of, dirs, files))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 167:
dirs[ino] = mkdir(m2, md1, # links(ino, dirs), m6, entries), entries0[str] = entries[str], dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), files[entries[str]] = mkfile(m1, md2, # links(entries[str], dirs), content0), dirs[ino1] = mkdir(m, md, # links(ino1, dirs), m4, entries1), c_inode = mkinode(entries[str], md2, false, # links(entries[str], dirs), 0, m1), err = err0, err0 = ESUCCESS, new_dent = negdentry(p.last), new_inode = mkinode(ino1, md, true, # links(ino1, dirs), m4, m), old_dent = mkdentry(str, entries0[str]), p_inode = new_inode, afs-cons(dirs, files), ispath(parent(p), ROOT_INO, ino1, dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md), px(user, md0), px-parent(user, parent(p), ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries, ino ∈ dirs, ino1 ∈ dirs, ino0 ∈ dirs, entries[str] ∈ files, str ∈ entries0, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ [if pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) then { let p_ino = p_inode.ino in {dirs[p_ino].entries[new_dent.name] := old_dent.ino; dirs[p_ino].size := dirs[p_ino].size + 1; let ino = old_dent.ino in afs_inc_nlink#(ino; dirs, files); new_dent := mkdentry(new_dent.name, old_dent.ino); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(old_dent.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort] (afs-cons(dirs, files) → of-cons(of, dirs, files)), p = ε, entries[str] ∈ dirs, p.last ∈ entries1

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_link# (OLD_DENT; P_INODE, C_INODE, NEW_DENT, ERR, DIRS, FILES; ASYNCED) {if pre-link(P_INODE, C_INODE, OLD_DENT, NEW_DENT, DIRS, FILES) then { let P_INO = P_INODE.ino in {DIRS[P_INO].entries[NEW_DENT.name] := OLD_DENT.ino; DIRS[P_INO].size := DIRS[P_INO].size + 1; let INO = OLD_DENT.ino in afs_inc_nlink#(INO; DIRS, FILES); NEW_DENT := mkdentry(NEW_DENT.name, OLD_DENT.ino); afs_inode_sync#(P_INODE; DIRS, FILES); afs_inode_sync#(C_INODE; DIRS, FILES); P_INODE := getinode(P_INODE.ino, DIRS, FILES); C_INODE := getinode(OLD_DENT.ino, DIRS, FILES); ERR := ESUCCESS} or fail#(; ; ERR); ASYNCED := ?} else abort };