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Proof step 381 from proof refine-link (previous step)

dirs0[ino3] = mkdir(# entries, md1, # links(ino3, dirs0), m4, entries), entries0[str] = entries[str], dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m2, entries0), files0[entries[str]] = mkfile(m0, md2, # links(entries[str], dirs0), content0), dirs0[ino2] = mkdir(# entries1, md, # links(ino2, dirs0), m3, entries1), root[q0].dir?, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs, files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)]), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), ispath(q0, ROOT_INO, ino2, dirs0, files0), of-cons(of, dirs, files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)]), of-cons(of, dirs0, files0), pw(user, md), px(user, md), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), px-parent(user, q0, ROOT_INO, dirs0, files0), str ∈ entries, ino3 ∈ dirs0, ino2 ∈ dirs0, ino1 ∈ dirs0, str ∈ entries0, entries[str] ∈ files0, dirs ≡ dirs0[ino2, mkdir(# entries1 + 1, md, # links(ino2, dirs0), m3, entries1[str0, entries[str]])], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ pre-link(q + str ', q0 + str0 ', ESUCCESS, user, root, abs-files(files0), abs-of(of)) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then let fid = root[q + str '].fid in root[q0 + str0 '] := fnode(fid); psynced := ?⟩ ( abs-files(files0) = abs-files (files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)] [entries0[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0) ]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), # links(ino2, dirs0) = 0, ino2 = ROOT_INO, links(ino2, dirs0) = ∅, root[q + str '].dir?, ino2 ∈ dirs, entries[str] ∈ dirs, entries[str] ∈ dirs0, str0 ∈ entries1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 382:
⊦ pre-link(p, p', ESUCCESS, user, root, fs, ofh) ↔ p ∈ root ∧ ¬ root[p].dir? ∧ ¬ p' ∈ root ∧ parent(p') ∈ root ∧ root[parent(p')].dir? ∧ px(user, parent(p), root, fs) ∧ py(user, parent(p'), root, fs)
Proof step 383:
dirs0[ino2] = mkdir(# entries1, md, # links(ino2, dirs0), m3, entries1), files0[entries[str]] = mkfile(m0, md2, # links(entries[str], dirs0), content0), dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m2, entries0), entries0[str] = entries[str], dirs0[ino3] = mkdir(# entries, md1, # links(ino3, dirs0), m4, entries), root.dir?, root[q].dir?, root[q0].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs, files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)]), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs0, files0), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs, files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)]), pw(user, md), px(user, md0), px(user, md), px-parent(user, q0, ROOT_INO, dirs0, files0), px-parent(user, q, ROOT_INO, dirs0, files0), entries[str] ∈ files0, str ∈ entries0, ino1 ∈ dirs0, ino2 ∈ dirs0, ino3 ∈ dirs0, str ∈ entries, dirs ≡ dirs0[ino2, mkdir(# entries1 + 1, md, # links(ino2, dirs0), m3, entries1[str0, entries[str]])], psynced → asynced0, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ( q + str ' ∈ root ∧ ¬ root[q + str '].dir? ∧ ¬ q0 + str0 ' ∈ root ∧ parent(q0 + str0 ') ∈ root ∧ root[parent(q0 + str0 ')].dir? ∧ px(user, parent(q + str '), root, abs-files(files0)) ∧ py(user, parent(q0 + str0 '), root, abs-files(files0))) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then let fid = root[q + str '].fid in root[q0 + str0 '] := fnode(fid); psynced := ?⟩ ( abs-files(files0) = abs-files (files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)] [entries0[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0) ]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), # links(ino2, dirs0) = 0, ino2 = ROOT_INO, links(ino2, dirs0) = ∅, root[q + str '].dir?, str0 ∈ entries1, entries[str] ∈ dirs0, entries[str] ∈ dirs, ino2 ∈ dirs

Rule argument

spec: posix-pre name: pre-link-esuccess seq: ⊦ pre-link(p, p', ESUCCESS, user, root, fs, ofh) ↔ p ∈ root ∧ ¬ root[p].dir? ∧ ¬ p' ∈ root ∧ parent(p') ∈ root ∧ root[parent(p')].dir? ∧ px(user, parent(p), root, fs) ∧ py(user, parent(p'), root, fs) subst: [ofh, fs, root, user, p', p] → [abs-of(of), abs-files(files0), root, user, q0 + str0 ', q + str '] flags: <all paths>

Additional information

Used terms: abs-of(of), abs-files(files0), root, user, q0 + str0 ', q + str '