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Proof step 160 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m1, # links(ino1, dirs0) = dirs0[ino1].nlink, dirs0[ino1] = mkdir(dirs0[ino1].size, md0, dirs0[ino1].nlink, dirs0[ino1].nsubdirs, entries0), files[entries0[str]] = mkfile(m, md1, m1, content0), entries0[str] = dirs0[ino1].entries[str], files[entries0[str]] = mkfile(m0, md, m1, content), dirs = dirs0[ino1, (dirs0[ino1].entries:= (dirs0[ino1].entries -- str)).size:= (dirs0[ino1].size - 1)], dom of < ino0, afs-cons(dirs0, files), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files), str ∈ entries0, entries0[str] ∈ files, ino1 ∈ dirs0, str ∈ dirs0[ino1].entries, 1 ≤ dirs0[ino1].size, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_drop_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(ino1, md0, true, dirs0[ino1].nlink, dirs0[ino1].nsubdirs, dirs0[ino1].size); dirs, files); afs_inode_sync#(mkinode(entries0[str], md1, false, # links(entries0[str], dirs0), 0, m); dirs, files); 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(entries0[str], dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → ⟪vfs_put_inode#(c_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))), dirs0[ino1].size = 0, entries0[str] ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 161:
# links(ino1, dirs0) = dirs0[ino1].nlink, entries0[str] = dirs0[ino1].entries[str], files[entries0[str]] = mkfile(m0, md, # links(entries0[str], dirs0), content), dirs0[ino1] = mkdir(dirs0[ino1].size, md0, dirs0[ino1].nlink, dirs0[ino1].nsubdirs, entries0), dirs = dirs0[ino1, (dirs0[ino1].entries:= (dirs0[ino1].entries -- str)).size:= (dirs0[ino1].size - 1)], dirs0[ino1].size ≠ 0, dom of < ino0, afs-cons(dirs0, files), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files), str ∈ dirs0[ino1].entries, ino1 ∈ dirs0, entries0[str] ∈ files, str ∈ entries0, 1 ≤ dirs0[ino1].size, ¬ entries0[str] ∈ dirs0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_drop_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(ino1, md0, true, dirs0[ino1].nlink, dirs0[ino1].nsubdirs, dirs0[ino1].size); dirs, files); afs_inode_sync#(mkinode(entries0[str], md, false, # links(entries0[str], dirs0), 0, m0); dirs, files); 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(entries0[str], dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → ⟪vfs_put_inode#(c_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)