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Proof step 360 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), dirs1[entries0[str]] = mkdir(m0, md0, m1, m4, entries), dirs0[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs0), m3, ∅), dirs0[ino1] = mkdir(m + 1, md2, # links(ino1, dirs0), m2, entries0), root[q + str '] = dnode(md1, ∅), err0 = ESUCCESS, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs, files), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), is-open(m5, of), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs, files), of-cons(of, dirs0, files), pw(user, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs0, files), entries0[str] ∈ dirs3, ino1 ∈ dirs2, str ∈ entries0, ino1 ∈ dirs0, entries0[str] ∈ dirs0, entries0[str] ∈ dirs1, dirs2 ≡ dirs1[entries0[str], mkdir(m0, md0, m1 - 1, m4, entries)], dirs1 ≡ dirs0[ino1, mkdir(m, md2, # links(ino1, dirs0), m2 - 1, entries0 -- str)], dirs3 ≡ dirs2[ino1, dirs2[ino1].meta:= md2], dirs ≡ dirs3[entries0[str], dirs3[entries0[str]].meta:= md], 1 ≤ m1, 1 ≤ m2, psynced0 → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ entries0 = ∅, m1 = 0, m2 = 0, ∃ psynced. abs(root -- (q + str '), ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 361:
⊦ ispath(p, ROOT_INO, ino, dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, m0, m1, entries) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ ¬ abs(tree0, ROOT_INO)(dirs0) → ( abs(tree, ROOT_INO)(dirs) ↔ (∃ sdt. ((abs|(tree, ROOT_INO, p, ino) * ino => mkdir(n, md, m0, m1, entries) * abs(sdt, entries)))(dirs) ∧ p ∈ tree ∧ tree[p] = dnode(md, sdt)))
Proof step 362:
⊦ str ∈ entries ∧ entries[str] ∈ dirs0 ∧ dirs1 ≡ dirs0[entries[str], ad] → (((abs(sdt, entries) * D))(dirs0) ↔ str ∈ sdt ∧ ((abs(sdt[str], entries[str]) * abs(sdt -- str, entries -- str) * D))(dirs0))
Proof step 363:
# 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), dirs0[ino1] = mkdir(m + 1, md2, # links(ino1, dirs0), m2, entries0), root[q] = dnode(md2, sdt), dirs1[entries0[str]] = mkdir(m0, md0, m1, m4, entries), dirs0[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs0), m3, ∅), root[q + str '] = dnode(md1, ∅), (( abs(sdt[str], entries0[str]) * abs(sdt -- str, entries0 -- str) * ino1 => mkdir(m, md2, # links(ino1, dirs0), m2 - 1, entries0 -- str) * abs|(root, ROOT_INO, q, ino1)) )(dirs1), root.dir?, dom of < ino0, afs-cons(dirs, files), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), is-open(m5, of), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs, files), of-cons(of, dirs0, files), pw(user, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs0, files), str ∈ sdt, entries0[str] ∈ dirs3, ino1 ∈ dirs2, str ∈ entries0, entries0[str] ∈ dirs0, entries0[str] ∈ dirs1, q ∈ root, ino1 ∈ dirs0, dirs2 ≡ dirs1[entries0[str], mkdir(m0, md0, m1 - 1, m4, entries)], dirs1 ≡ dirs0[ino1, mkdir(m, md2, # links(ino1, dirs0), m2 - 1, entries0 -- str)], dirs3 ≡ dirs2[ino1, dirs2[ino1].meta:= md2], dirs ≡ dirs3[entries0[str], dirs3[entries0[str]].meta:= md], 1 ≤ m1, 1 ≤ m2, psynced0 → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ entries0 = ∅, m1 = 0, m2 = 0, abs(root -- (q + str '), ROOT_INO)(dirs)

Rule argument

Additional information

Used simplifier rules: abs-unfold: ⊦ ispath(p, ROOT_INO, ino, dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, m0, m1, entries) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ ¬ abs(tree0, ROOT_INO)(dirs0) → ( abs(tree, ROOT_INO)(dirs) ↔ (∃ sdt. (( abs|(tree, ROOT_INO, p, ino) * ino => mkdir(n, md, m0, m1, entries) * abs(sdt, entries)) )(dirs) ∧ p ∈ tree ∧ tree[p] = dnode(md, sdt)));%abs-unfold-entry-p: ⊦ str ∈ entries ∧ entries[str] ∈ dirs0 ∧ dirs1 ≡ dirs0[entries[str], ad] → ( ((abs(sdt, entries) * D))(dirs0) ↔ str ∈ sdt ∧ (( abs(sdt[str], entries[str]) * abs(sdt -- str, entries -- str) * D) )(dirs0));% ⊦ dnode(md, sdt).dir?; (s)%⊦ dirs ≡ dirs0[ino, ad] → ( ((ino => ad0 * D))(dirs0) ↔ ((ino => ad * D))(dirs) ∧ dirs0[ino] = ad0 ∧ ino ∈ dirs0); (ws)% ⊦ ((ino => ad * D))(dirs) → ino ∈ dirs; (s)% ⊦ ((ino => ad * D))(dirs) → (dirs[ino] = ad0 ↔ ad = ad0); (s)%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap]%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]