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Proof step 235 from proof refine-unlink (previous step)

# links(ino1, dirs0) = dirs0[ino1].nlink, # links(entries[str], dirs0) = files[entries[str]].nlink, # entries = m0 + 1, m0 + 1 = dirs0[ino1].size, entries[str] = dirs0[ino1].entries[str], files[entries[str]] = mkfile(m, md0, files[entries[str]].nlink, content), dirs0[ino1] = mkdir(m0 + 1, md, dirs0[ino1].nlink, dirs0[ino1].nsubdirs, entries), fs = abs-files(files), entries ≠ ∅, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs0, files), str ∈ dirs0[ino1].entries, entries[str] ∈ files, ino1 ∈ dirs0, str ∈ entries, dirs ≡ dirs0[ino1, (dirs0[ino1].entries:= (dirs0[ino1].entries -- str)).size:= m0], ¬ root[q + str '].dir?, ¬ entries[str] ∈ dirs, ¬ entries[str] ∈ dirs0, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(ino1, md, true, dirs0[ino1].nlink, dirs0[ino1].nsubdirs, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries[str], md0, false, # links(entries[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(entries[str], dirs, files); err := ESUCCESS; asynced := ?; vfs_put_inode#(c_inode, of, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_unlink#(q + str ', user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 236:
# entries = m0 + 1, # links(entries[str], dirs0) = m2, # links(ino1, dirs0) = dirs0[ino1].nlink, m0 + 1 = dirs0[ino1].size, dirs0[ino1] = mkdir(m0 + 1, md, dirs0[ino1].nlink, dirs0[ino1].nsubdirs, entries), files[entries[str]] = mkfile(m, md0, m2, content), entries[str] = dirs0[ino1].entries[str], files[entries[str]] = mkfile(m1, md1, m2, content0), fs = abs-files(files), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs0, files), str ∈ entries, ino1 ∈ dirs0, entries[str] ∈ files, str ∈ dirs0[ino1].entries, dirs ≡ dirs0[ino1, (dirs0[ino1].entries:= (dirs0[ino1].entries -- str)).size:= m0], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(ino1, md, true, dirs0[ino1].nlink, dirs0[ino1].nsubdirs, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries[str], md0, false, # links(entries[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(entries[str], dirs, files); err := ESUCCESS; asynced := ?; vfs_put_inode#(c_inode, of, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_unlink#(q + str ', user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1)), entries = ∅, root[q + str '].dir?, entries[str] ∈ dirs, entries[str] ∈ dirs0

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[entries[str]], m1, md1, m2, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[entries[str]], m1, md1, m2, content0