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Proof step 161 from proof inv-unlink (previous step)

# 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)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 162:
# links(ino1, dirs0) = m1, dirs0[ino1] = mkdir(m, md0, m1, m2, entries0), files[entries0[str]] = mkfile(m0, md, # links(entries0[str], dirs0), content), entries0[str] = entries[str], dirs0[ino1] = mkdir(m, md1, m1, m2, entries), dirs = dirs0[ino1, (dirs0[ino1].entries:= (entries -- str)).size:= (m - 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 ∈ entries, 1 ≤ m, 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, m1, m2, m); 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))), m = 0, entries0[str] ∈ dirs0

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs0[ino1], m, md1, m1, m2, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs0[ino1], m, md1, m1, m2, entries