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Proof step 13 from proof inv-recover (previous step)

dirs = dirs0 \ orphans(dirs0, files1), files = files1 \ orphans(dirs0, files1), dom of < ino, afs-cons(dirs0, files1), of-cons(of, dirs0, files1) ⊦ [asynced := true, err := ESUCCESS] (asynced ∧ afs-cons(dirs, files) → err = ESUCCESS → of-cons(∅, dirs, files))

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 14:
⊦ of-cons(of0, dirs0, files0) → (of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1))

Rule argument

Additional information

Used simplifier rules: of-cons-reduce: ⊦ of-cons(of0, dirs0, files0) → ( of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1));% ⊦ ¬ fd ∈ ∅; (s)