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Proof step 174 from proof inv-link (previous step)

dirs0[ino1] = mkdir(m, md, # links(ino1, dirs0), m4, entries1), files[entries[str]] = mkfile(m1, md2, # links(entries[str], dirs0), content0), dirs0[ino0] = mkdir(m0, md0, # links(ino0, dirs0), m3, entries0), entries0[str] = entries[str], dirs0[ino2] = mkdir(m2, md1, # links(ino2, dirs0), m6, entries), c_inode = mkinode(entries[str], md2, false, # links(entries[str], dirs0), 0, m1), dirs = dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[new_dent.name, old_dent.ino]] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[new_dent.name, old_dent.ino]][p_ino] .size:= (dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[new_dent.name, old_dent.ino]][p_ino].size + 1) ], err = err0, err0 = ESUCCESS, ino = old_dent.ino, new_dent = negdentry(p.last), new_inode = mkinode(ino1, md, true, # links(ino1, dirs0), m4, m), old_dent = mkdentry(str, entries0[str]), p_ino = p_inode.ino, p_inode = new_inode, old_dent.dentry?, afs-cons(dirs0, files), ispath(q, ROOT_INO, ino0, dirs0, files), ispath(parent(p), ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pre-link(p_inode, c_inode, old_dent, new_dent, dirs0, files), pw(user, md), px(user, md0), px(user, md), px-parent(user, q, ROOT_INO, dirs0, files), px-parent(user, parent(p), ROOT_INO, dirs0, files), str ∈ entries0, entries[str] ∈ files, ino0 ∈ dirs0, ino1 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ [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; asynced := ?] (afs-cons(dirs, files) → of-cons(of, dirs, files)), p = ε, p.last ∈ entries1, entries[str] ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 175:
# links(entries[str], dirs0) = files[entries[str]].nlink, # links(ino1, dirs0) = dirs0[ino1].nlink, entries[str] = dirs0[ino].entries[str], dirs0[ino1] = mkdir(dirs0[ino1].size, md, dirs0[ino1].nlink, dirs0[ino1].nsubdirs, entries1), files[entries[str]] = mkfile(m1, md2, files[entries[str]].nlink, content0), dirs0[ino0] = mkdir(m0, md0, # links(ino0, dirs0), m3, entries0), entries0[str] = entries[str], dirs0[ino2] = mkdir(m2, md1, # links(ino2, dirs0), m6, entries), dirs = dirs0[ino1, (dirs0[ino1].entries:= dirs0[ino1].entries[p.last, entries[str]]).size:= (dirs0[ino1].size + 1)], p ≠ ε, afs-cons(dirs0, files), ispath(q, ROOT_INO, ino0, dirs0, files), ispath(parent(p), ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md), px(user, md0), px(user, md), px-parent(user, q, ROOT_INO, dirs0, files), px-parent(user, parent(p), ROOT_INO, dirs0, files), str ∈ dirs0[ino].entries, ino ∈ dirs0, str ∈ entries0, entries[str] ∈ files, ino0 ∈ dirs0, ino1 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries, ¬ p.last ∈ dirs0[ino1].entries, ¬ p.last ∈ entries1, ¬ entries[str] ∈ dirs0, links(ino, dirs0) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ [afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); new_dent := mkdentry(p.last, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(ino1, md, true, dirs0[ino1].nlink, dirs0[ino1].nsubdirs, dirs0[ino1].size); dirs, files); afs_inode_sync#(mkinode(entries[str], md2, false, # links(entries[str], dirs0), 0, m1); dirs, files); new_inode := (ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → of-cons(of, dirs, files))

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ 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)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)% ⊦ negdentry(str).negdentry?; (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)%⊦ valid-dentry(dent, dirs, files) ↔ (∃ ino. valid-dentry(ino, dent, dirs, files)); (s)%⊦ pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) ↔ valid-dentry(old_dent, dirs, files) ∧ valid-negdentry(p_inode.ino, new_dent, dirs, files) ∧ (links(old_dent.ino, dirs) ≠ ∅ ∨ old_dent.ino = ROOT_INO) ∧ valid-dir-inode(p_inode, dirs, files) ∧ valid-file-inode(c_inode, dirs, files) ∧ c_inode.ino = old_dent.ino; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)% ⊦ (ad.entries:= entries).size = ad.size; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ negdentry(str).name = str; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)