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Proof step 198 from proof refine-create (previous step)

dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m3, entries0), fs = abs-files(files0), path = q + str ', # links(ino1, dirs0) ≠ 0, ino1 ≠ ROOT_INO, ino2 ≠ 0, links(ino1, dirs0) ≠ ∅, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), of-cons(of, dirs0, files0), 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 ∈ dirs, ¬ ino1 ∈ dirs, ¬ ino2 ∈ dirs0, ¬ ino2 ∈ files0, ¬ str ∈ entries0, psynced → asynced0 ⊦ ∃ 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: separation, inst: dir-heap name: eq seq: ⊦ dirs ≡ dirs0 ↔ dirs = dirs0 subst: [dirs0, dirs] → [dirs0 [ino1, mkdir (# entries0 + 1, md0, # links(ino1, dirs0), m3, entries0[str, ino2]) ], dirs] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s) Used terms: dirs0 [ino1, mkdir (# entries0 + 1, md0, # links(ino1, dirs0), m3, entries0[str, ino2]) ], dirs