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Proof step 292 from proof refine-link (previous step)

dirs0[ino3] = mkdir(# entries, md1, # links(ino3, dirs0), m4, entries), entries0[str] = entries[str], dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m2, entries0), files[entries[str]] = mkfile(m0, md2, # links(entries[str], dirs0), content0), dirs0[ino2] = mkdir(# entries1, md, # links(ino2, dirs0), m3, entries1), fs = abs-files(files), ino = mkdentry(str, entries0[str]).ino, mkdentry(str, entries0[str]).dentry?, root[q0].dir?, 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), ispath(q0, ROOT_INO, ino2, dirs0, files), of-cons(of, dirs0, files), pw(user, md), px(user, md), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files), px-parent(user, q0, ROOT_INO, dirs0, files), str ∈ entries, ino3 ∈ dirs0, ino2 ∈ dirs0, ino1 ∈ dirs0, entries[str] ∈ files, 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 ⊦ [if ino ∈ dirs then dirs[ino].nlink := dirs[ino].nlink + 1; if ino ∈ files then files[ino].nlink := files[ino].nlink + 1; new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(ino2, md, true, # links(ino2, dirs0), m3, # entries1); dirs, files); 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, fs, abs-of(of); err2, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)), root[q + str '].dir?, entries[str] ∈ dirs, entries[str] ∈ dirs0, str0 ∈ entries1

Heuristic symbolic execution applied rule if negative right

And obtained the following new goals

Proof step 293:
dirs0[ino2] = mkdir(# entries1, md, # links(ino2, dirs0), m3, entries1), files[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), fs = abs-files(files), ino = mkdentry(str, entries0[str]).ino, mkdentry(str, entries0[str]).dentry?, root.dir?, root[q].dir?, root[q0].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs0, files), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md), px(user, md0), px(user, md), px-parent(user, q0, ROOT_INO, dirs0, files), px-parent(user, q, ROOT_INO, dirs0, files), str ∈ entries0, entries[str] ∈ files, ino1 ∈ dirs0, ino2 ∈ dirs0, ino3 ∈ dirs0, str ∈ entries, dirs ≡ dirs0[ino2, mkdir(# entries1 + 1, md, # links(ino2, dirs0), m3, entries1[str0, entries[str]])], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ [skip; if ino ∈ files then files[ino].nlink := files[ino].nlink + 1; new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(ino2, md, true, # links(ino2, dirs0), m3, # entries1); dirs, files); 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, fs, abs-of(of); err2, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)), root[q + str '].dir?, str0 ∈ entries1, entries[str] ∈ dirs0, entries[str] ∈ dirs

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).ino = m; (s)