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Proof step 307 from proof refine-link (previous step)

dirs0[ino2] = mkdir(# entries1, md, # links(ino2, dirs0), m3, entries1), files0[entries[str]] = mkfile(m0, md2, # links(entries[str], dirs0), content0), dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m2, entries0), entries0[str] = entries[str], dirs0[ino3] = mkdir(# entries, md1, # links(ino3, dirs0), m4, entries), files = files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)], root.dir?, root[q].dir?, root[q0].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs0, files0), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md), px(user, md0), px(user, md), px-parent(user, q0, ROOT_INO, dirs0, files0), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ entries0, entries[str] ∈ files0, ino1 ∈ dirs0, ino3 ∈ dirs0, str ∈ entries, ino2 ∈ dirs0, dirs ≡ dirs0[ino2, mkdir(# entries1 + 1, md, # links(ino2, dirs0), m3, entries1[str0, entries[str]])], ¬ root[q + str '].dir?, ¬ str0 ∈ entries1, ¬ entries[str] ∈ dirs0, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(entries0[str], md2, false, # links(entries0[str], dirs0), 0, m0); dirs, files); new_inode := (ino2 ∈ dirs ⊃ mkinode(ino2, dirs[ino2].meta, true, dirs[ino2].nlink, dirs[ino2].nsubdirs, dirs[ino2].size) ;mkinode(ino2, files[ino2].meta, false, files[ino2].nlink, 0, files[ino2].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', q0 + str0 ', user, abs-files(files0), abs-of(of); err2, root; psynced)⟩ (abs-files(files0) = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 308:
dirs0[ino3] = mkdir(# entries, md1, # links(ino3, dirs0), m4, entries), entries0[str] = entries[str], dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m2, entries0), files0[entries[str]] = mkfile(m0, md2, # links(entries[str], dirs0), content0), dirs0[ino2] = mkdir(# entries1, md, # links(ino2, dirs0), m3, entries1), files = files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)], inode = mkinode(entries0[str], md2, false, # links(entries0[str], dirs0), 0, m0), root[q0].dir?, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), ispath(q0, ROOT_INO, ino2, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md), px(user, md), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), px-parent(user, q0, ROOT_INO, dirs0, files0), ino2 ∈ dirs0, str ∈ entries, ino3 ∈ dirs0, ino1 ∈ dirs0, entries[str] ∈ files0, str ∈ entries0, dirs ≡ dirs0[ino2, mkdir(# entries1 + 1, md, # links(ino2, dirs0), m3, entries1[str0, entries[str]])], psynced → asynced0, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [let ino = inode.ino in if ino ∈ files then {files[ino].size := inode.size; files[ino].meta := inode.meta} else if ino ∈ dirs then dirs[ino].meta := inode.meta; new_inode := (ino2 ∈ dirs ⊃ mkinode(ino2, dirs[ino2].meta, true, dirs[ino2].nlink, dirs[ino2].nsubdirs, dirs[ino2].size) ;mkinode(ino2, files[ino2].meta, false, files[ino2].nlink, 0, files[ino2].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', q0 + str0 ', user, abs-files(files0), abs-of(of); err2, root; psynced)⟩ (abs-files(files0) = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)), root[q + str '].dir?, str0 ∈ entries1, entries[str] ∈ dirs0

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_inode_sync#(INODE; DIRS, FILES) {let INO = INODE.ino in if INO ∈ FILES then {FILES[INO].size := INODE.size; FILES[INO].meta := INODE.meta} else if INO ∈ DIRS then DIRS[INO].meta := INODE.meta };