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Proof step 3 from proof of-cons-file (previous step)

of[fd] = mkfile(ino, mode, n), of-cons(of, dirs, files), fd ∈ of ⊦ ino ∈ files

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ of-cons(of, dirs, files) ↔ (∀ n. n ∈ of → of[n].ino ∈ files)
Proof step 5:
of[fd] = mkfile(ino, mode, n), fd ∈ of, ∀ n. n ∈ of → of[n].ino ∈ files ⊦ ino ∈ files

Rule argument

spec: <toplevel> name: of-cons seq: ⊦ of-cons(of, dirs, files) ↔ (∀ n. n ∈ of → of[n].ino ∈ files) subst: [files, dirs, of] → [files, dirs, of] flags: <all paths>

Additional information

Used terms: files, dirs, of