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Proof step 16 from proof of-cons-reduce (previous step)

of1[n] = mkfile(m, mode, m0), n ∈ of1, (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1, ∀ n. n ∈ of0 → of0[n].ino ∈ files0 ⊦ m ∈ files1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
of1[n] = mkfile(m, mode, m0), n ∈ of1, n ∈ of0, ∀ n. n ∈ of0 → of0[n].ino ∈ files0 ⊦ m ∈ files1, of0[n].ino ∈ files0

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, mode, m0).ino = m; (s)