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Proof step 351 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, boolvar, m6, m7, m8), 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)), is-open(m5, 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), entries0[str] ∈ dirs1, entries0[str] ∈ dirs0, ino1 ∈ dirs0, str ∈ entries0, ino1 ∈ dirs2, entries0[str] ∈ dirs3, dirs ≡ dirs3[entries0[str], dirs3[entries0[str]].meta:= md], dirs3 ≡ dirs2[ino1, dirs2[ino1].meta:= md2], dirs1 ≡ dirs0[ino1, mkdir(m, md2, # links(ino1, dirs0), m2 - 1, entries0 -- str)], dirs2 ≡ dirs1[entries0[str], mkdir(m0, md0, m1 - 1, m4, entries)], 1 ≤ m2, 1 ≤ m1, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ 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), entries0 = ∅, m1 = 0, m2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 352:
⊦ 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 353:
⊦ 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 354:
# 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, boolvar, m6, m7, m8), 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), entries0 ≠ ∅, m1 ≠ 0, m2 ≠ 0, 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)), is-open(m5, 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), entries0[str] ∈ dirs1, entries0[str] ∈ dirs0, ino1 ∈ dirs0, str ∈ entries0, ino1 ∈ dirs2, entries0[str] ∈ dirs3, dirs ≡ dirs3[entries0[str], dirs3[entries0[str]].meta:= md], dirs3 ≡ dirs2[ino1, dirs2[ino1].meta:= md2], dirs1 ≡ dirs0[ino1, mkdir(m, md2, # links(ino1, dirs0), m2 - 1, entries0 -- str)], dirs2 ≡ dirs1[entries0[str], mkdir(m0, md0, m1 - 1, m4, entries)], 1 ≤ m2, 1 ≤ m1, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ 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)