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Proof step 416 from proof refine-unlink (previous step)

⟨dirs := dirs -- ino⟩ (ESUCCESS = err0 ∧ dirs = dirs1 ∧ files = files1), # entries0 = m0 + 1, # links(entries0[str], dirs0) = m + 1, dirs[ino].nlink = 0, files0[entries0[str]] = mkfile(m1, md1, m + 1, content0), dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), err = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], fs = abs-files(files0), ino = inode.ino, inode = getinode(entries0[str], dirs, files), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs1, files1), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs1, files1), of-cons(of, dirs0, files0), pre-evict(inode, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino ∈ dirs, str ∈ entries0, entries0[str] ∈ files0, ino1 ∈ dirs0, dirs ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_unlink#(q + str ', user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files1) ∧ abs(root, ROOT_INO)(dirs1) ∧ (psynced → asynced) ∧ err0 = err1), dirs = dirs1, entries0 = ∅, root[q + str '].dir?, is-open ((entries0[str] ∈ dirs ⊃ mkinode(entries0[str], dirs[entries0[str]].meta, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size) ;mkinode(entries0[str], md1, false, m, 0, m1) ) .ino, of), entries0[str] ∈ dirs0

Heuristic symbolic execution applied rule assign left

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: abs-acyclic: ⊦ abs(tree, ROOT_INO)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, m, m0, entries) ∧ str ∈ entries ∧ ispath(p, ROOT_INO, ino, dirs, files) → entries[str] ≠ ROOT_INO;%⊦ 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)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).size = m; (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)% ⊦ 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)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)%⊦ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) → abs-files(files[ino, mkfile(m, md, n1, content)]) = abs-files(files); (s)%assign-new-other: ⊦ dirs ≡ dirs0[ino, ad] ∧ ¬ ino0 ∈ dirs0 ∧ ino ∈ dirs0 → ¬ ino0 ∈ dirs; (forward) from specification separation[dir-heap]% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ ¬ ino ∈ dirs → dirs -- ino = dirs; (s)% ⊦ dirs ≠ dirs0 → ¬ dirs ≡ dirs0; (s)