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Proof step 3 from proof recovery (previous step)

dirs = dirs0 \ orphans(dirs0, files), files0 = files \ orphans(dirs0, files), tree0.dir?, dom of < ino, abs(tree0, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(tree0, abs-files(files), abs-of(of)), of-cons(of, dirs0, files) ⊦ ⟪vfs_recover#(isdir2; dirs, files0, asynced; of0, ino0, err)⟫ ( ( err = ESUCCESS → (∃ root, fs, ofh. posix-crash(tree0, abs-files(files), abs-of(of), root, fs, ofh) ∧ ⟨posix_recover#(isdir2; root, fs, ofh; psynced, err0)⟩ (ofh = abs-of(of0) ∧ fs = abs-files(files0) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0))) ∧ ( err ≠ ESUCCESS → (∀ tree, fs, ofh, isdir. ⟨posix_recover#(isdir2; root0, fs1, ofh1; psynced0, err0)⟩ (tree = root0 ∧ fs = fs1 ∧ ofh = ofh1 ∧ (isdir ↔ psynced0) ∧ err = err0))))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: vfs-asm name: inv-recover seq: dirs = dirs0 \ orphans(dirs0, files), files0 = files \ orphans(dirs0, files), isdir, of-cons(of, dirs0, files), dom of < ino, afs-cons(dirs0, files) ⊦ ⟪vfs_recover# (isdir0; dirs, files0, asynced; of0, ino0, err)⟫ ( err = ESUCCESS → asynced ∧ of-cons(of0, dirs, files0) ∧ dom of0 < ino0 ∧ afs-cons(dirs, files0)) subst: [isdir0, asynced, files0, dirs, err, ino0, of0, isdir, dirs0, files, of, ino] → [isdir2, asynced, files0, dirs, err, ino0, of0, true, dirs0, files, of, ino] flags: <all paths>

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