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Proof step 171 from proof refine-create (previous step)

dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m3, entries0), err0 = err2, fs = abs-files(files0), ofh = abs-of(of), path = q + str ', root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino1 ∈ dirs0, dirs ≡ dirs0[ino1, mkdir(# entries0 + 1, md0, # links(ino1, dirs0), m3, entries0[str, ino2])], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ∃ err. pre-create(path, md, err, user, root, fs, ofh) ∧ ⟨err0 := err; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files((files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), ino2 = 0, ino2 ∈ dirs0, ino2 ∈ dirs, str ∈ entries0, ino2 ∈ files0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 172:
dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m3, entries0), fs = abs-files(files0), path = q + str ', ino2 ≠ 0, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino1 ∈ dirs0, dirs ≡ dirs0[ino1, mkdir(# entries0 + 1, md0, # links(ino1, dirs0), m3, entries0[str, ino2])], ¬ ino2 ∈ dirs0, ¬ ino2 ∈ dirs, ¬ str ∈ entries0, ¬ ino2 ∈ files0, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ∃ err. pre-create(path, md, err, user, root, fs, abs-of(of)) ∧ ⟨err0 := err; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files((files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ str ∈ str0 ' ↔ str = str0; (s)% ⊦ str ∈ p + p0 ↔ str ∈ p ∨ str ∈ p0; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]%in-15: ⊦ p + str ' = p0 → str ∈ p0; (forward) from specification list[path]