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Proof step 523 from proof refine-rmdir (previous step)

# entries0 = m + 1, root[q + str '] = dnode(md1, ∅), dirs0[ino1] = mkdir(m + 1, md2, # links(ino1, dirs0), m5 + 1, entries0), dirs0[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs0), m3, ∅), dirs1[entries0[str]] = mkdir(m0, md0, m2 + 1, m4, entries), err = ESUCCESS, fs = abs-files(files), inode = getinode(entries0[str], dirs, files), 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, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs0, files), entries0[str] ∈ dirs1, entries0[str] ∈ dirs0, ino1 ∈ dirs0, str ∈ entries0, dirs1 ≡ dirs0[ino1, mkdir(m, md2, # links(ino1, dirs0), m5, entries0 -- str)], dirs ≡ dirs1[entries0[str], mkdir(m0, md0, m2, m4, entries)], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [if pre-evict(inode, dirs, files) then {err := ESUCCESS; let ino = inode.ino in if ino ∈ dirs then if dirs[ino].nlink = 0 then dirs := dirs -- ino else if files[ino].nlink = 0 then files := files -- ino} else abort] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(q + str ', user, fs, abs-of(of); err1, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1)), entries0 = ∅, ino1 ∈ dirs, entries0[str] ∈ dirs

Heuristic symbolic execution applied rule if negative right

And obtained the following new goals

Proof step 524:
# entries0 = m + 1, dirs1[entries0[str]] = mkdir(m0, md0, m2 + 1, m4, entries), dirs0[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs0), m3, ∅), dirs0[ino1] = mkdir(m + 1, md2, # links(ino1, dirs0), m5 + 1, entries0), root[q + str '] = dnode(md1, ∅), err = ESUCCESS, fs = abs-files(files), inode = getinode(entries0[str], dirs, 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, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs0, files), str ∈ entries0, ino1 ∈ dirs0, entries0[str] ∈ dirs0, entries0[str] ∈ dirs1, dirs ≡ dirs1[entries0[str], mkdir(m0, md0, m2, m4, entries)], dirs1 ≡ dirs0[ino1, mkdir(m, md2, # links(ino1, dirs0), m5, entries0 -- str)], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [abort] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(q + str ', user, fs, abs-of(of); err1, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1)), entries0 = ∅, entries0[str] ∈ dirs, ino1 ∈ dirs

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ pre-evict(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files) ∧ inode.ino ≠ ROOT_INO; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)