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Proof step 8 from proof dir-not-open (previous step)

afs-cons(dirs, files), n ∈ of, of[n].ino ∈ dirs, ∀ n. n ∈ of → of[n].ino ∈ files ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
of[n] = mkfile(m, mode, m0), afs-cons(dirs, files), m ∈ dirs, n ∈ of, ∀ n. n ∈ of → of[n].ino ∈ files ⊦

Rule argument

spec: file name: elim seq: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0) subst: [file, m, mode, m0] → [of[n], m, mode, m0]

Additional information

Used simplifier rules: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of[n], m, mode, m0