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Proof step 556 from proof refine-unlink (previous step)

⟨if ¬ is-open(entries0[str], of) ∧ ¬ ⌜entries0[str]⌝ ∈ (root0 -- (q + str ')).fids then fs := fs -- ⌜entries0[str]⌝ ⟩ (fs = fs0), # links(entries0[str], dirs0) = m + 1, # entries0 = m0 + 1, dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m1, md1, m + 1, content0), dirs = dirs1, err = err0, err = ESUCCESS, err0 = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], files = files1, fs = abs-files(files0), p_inode = getinode(entries0[str], dirs1, files), root0.dir?, root0[q].dir?, dom of < ino0, abs(root0, ROOT_INO)(dirs0), abs(root0 -- (q + str '), ROOT_INO)(dirs1), afs-cons(dirs1, files1), afs-cons(dirs0, files0), fids-cons(root0, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs1, files1), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), entries0[str] ∈ files0, ino1 ∈ dirs0, str ∈ entries0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], psynced → asynced0 ⊦ ⟨psynced := ?⟩ ((root0 -- (q + str ')).dir? ∧ fids-cons(root0 -- (q + str '), fs0, abs-of(of)) → fs0 = abs-files(files1) ∧ (psynced → asynced)), # links(ino1, dirs0) = 0, entries0 = ∅, ino1 = ROOT_INO, links(ino1, dirs0) = ∅, root0[q + str '].dir?, entries0[str] ∈ dirs0, ino1 ∈ dirs1, entries0[str] ∈ dirs1, err = ESUCCESS ∧ ¬ is-open(p_inode.ino, of)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 557:
⟨skip⟩ (abs-files(files0) = fs0), # links(entries0[str], dirs0) = m + 1, # entries0 = m0 + 1, dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m1, md1, m + 1, content0), # links(ino1, dirs0) ≠ 0, entries0 ≠ ∅, ino1 ≠ ROOT_INO, links(ino1, dirs0) ≠ ∅, root0.dir?, root0[q].dir?, dom of < ino0, abs(root0, ROOT_INO)(dirs0), abs(root0 -- (q + str '), ROOT_INO)(dirs1), afs-cons(dirs1, files0[entries0[str], mkfile(m1, md1, m, content0)]), afs-cons(dirs0, files0), fids-cons(root0, abs-files(files0), abs-of(of)), is-open(entries0[str], of), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs1, files0[entries0[str], mkfile(m1, md1, m, content0)]), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), entries0[str] ∈ files0, ino1 ∈ dirs0, str ∈ entries0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], ¬ root0[q + str '].dir?, ¬ entries0[str] ∈ dirs0, ¬ ino1 ∈ dirs1, ¬ entries0[str] ∈ dirs1, psynced → asynced0 ⊦ ⟨psynced := ?⟩ ((root0 -- (q + str ')).dir? ∧ fids-cons(root0 -- (q + str '), fs0, abs-of(of)) → fs0 = abs-files(files0) ∧ (psynced → asynced))

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) → abs-files(files[ino, mkfile(m, md, n1, content)]) = abs-files(files); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)%⊦ 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)