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Proof step 437 from proof refine-rmdir (previous step)

# entries0 = m + 1, (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], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ) = mkinode(m5, md3, true, # links(m5, dirs), m8, # entries1), dirs[m5] = mkdir(# entries1, md4, # links(m5, dirs), m8, entries1), root[q + str '] = dnode(md1, ∅), dirs0[ino1] = mkdir(m + 1, md2, # links(ino1, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs0), m3, ∅), dirs1[entries0[str]] = mkdir(m0, md0, m1, m4, entries), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), of-cons(of, dirs, files), pw(user, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs0, files), m5 ∈ dirs, entries0[str] ∈ dirs1, entries0[str] ∈ dirs0, ino1 ∈ dirs0, str ∈ entries0, dirs ≡ dirs1[entries0[str], mkdir(m0, md, m1 - 1, m4, entries)], dirs1 ≡ dirs0[ino1, mkdir(m, md2, # links(ino1, dirs0), m2 - 1, entries0 -- str)], 1 ≤ m2, 1 ≤ m1, psynced → asynced0 ⊦ pre-rmdir(q + str ', ESUCCESS, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then root := root -- (q + str '); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), ∃ err. pre-rmdir(q + str ', err, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := err; if err0 = ESUCCESS then root := root -- (q + str '); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), # links(m5, dirs) = 0, # links(ino1, dirs0) = 0, entries0 = ∅, ino1 = ROOT_INO, links(m5, dirs) = ∅, links(ino1, dirs0) = ∅, m1 = 0, m2 = 0, m5 = ROOT_INO, ino1 ∈ dirs1, ino1 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 438:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p + str ' ∈ tree ↔ m ∈ dirs ∧ str ∈ dirs[m].entries)
Proof step 439:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (py(user, p, tree, abs-files(files)) ↔ py(user, p, ino, dirs, files))
Proof step 440:
# entries0 = m + 1, (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], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ) = mkinode(m5, md3, true, # links(m5, dirs), m8, # entries1), dirs[m5] = mkdir(# entries1, md4, # links(m5, dirs), m8, entries1), root[q + str '] = dnode(md1, ∅), dirs0[ino1] = mkdir(m + 1, md2, # links(ino1, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs0), m3, ∅), dirs1[entries0[str]] = mkdir(m0, md0, m1, m4, entries), # links(m5, dirs) ≠ 0, # links(ino1, dirs0) ≠ 0, entries0 ≠ ∅, ino1 ≠ ROOT_INO, links(m5, dirs) ≠ ∅, links(ino1, dirs0) ≠ ∅, m1 ≠ 0, m2 ≠ 0, m5 ≠ ROOT_INO, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), of-cons(of, dirs, files), pw(user, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs0, files), m5 ∈ dirs, entries0[str] ∈ dirs1, entries0[str] ∈ dirs0, ino1 ∈ dirs0, str ∈ entries0, dirs ≡ dirs1[entries0[str], mkdir(m0, md, m1 - 1, m4, entries)], dirs1 ≡ dirs0[ino1, mkdir(m, md2, # links(ino1, dirs0), m2 - 1, entries0 -- str)], 1 ≤ m2, 1 ≤ m1, ¬ ino1 ∈ dirs1, ¬ ino1 ∈ dirs, psynced → asynced0 ⊦ ∃ err. pre-rmdir(q + str ', err, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := err; if err0 = ESUCCESS then root := root -- (q + str '); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), py(user, q, ROOT_INO, dirs0, files) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then root := root -- (q + str '); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: path-in-last: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p + str ' ∈ tree ↔ m ∈ dirs ∧ str ∈ dirs[m].entries);%py: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( py(user, p, tree, abs-files(files)) ↔ py(user, p, ino, dirs, files));% ⊦ dnode(md, sdt).entries = sdt; (s)% ⊦ dnode(md, sdt).dir?; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ parent(p + str ') = p; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p + str ' ≠ ε; (s)%⊦ pre-rmdir(p, ESUCCESS, user, root, fs, ofh) ↔ p ≠ ε ∧ p ∈ root ∧ root[p].dir? ∧ root[p].entries = ∅ ∧ py(user, parent(p), root, fs); (s)