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Proof step 296 from proof refine-unlink (previous step)

⟨files := files -- ino⟩ (ESUCCESS = err2 ∧ dirs = dirs1 ∧ files = files1), # links(entries0[str], dirs0) = m + 1, # entries0 = m0 + 1, files[ino].nlink = 0, dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m1, md1, m + 1, content0), dirs = dirs1, err = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], ino = inode.ino, inode = getinode(entries0[str], dirs1, files), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs1, files1), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs1, files1), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ entries0, ino1 ∈ dirs0, entries0[str] ∈ files0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ entries0 = ∅, root[q + str '].dir?, is-open(entries0[str], of), pre-unlink(q + str ', err2, user, root, abs-files(files0), abs-of(of)), ino ∈ dirs, entries0[str] ∈ dirs0, entries0[str] ∈ dirs1

Heuristic symbolic execution applied rule assign left

And obtained the following new goals

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));%py-strong: ⊦ ispath(q, ino, m, dirs, files) ∧ px-parent(user, q, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( py(user, q, ino, dirs, files) ↔ pw(user, meta(ε, m, dirs, files)) ∧ px(user, meta(ε, m, dirs, files)));%⊦ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)%ino ∈ files ⊦ files[ino, af] -- ino = files -- ino; (s)%⊦ pre-unlink(p, ESUCCESS, user, root, fs, ofh) ↔ p ≠ ε ∧ p ∈ root ∧ ¬ root[p].dir? ∧ py(user, parent(p), root, fs); (s)% ⊦ p + str ' ≠ ε; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ parent(p + str ') = p; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ ino ∈ dirs → meta(ε, ino, dirs, files) = dirs[ino].meta; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)