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Proof step 17 from proof inv-open (previous step)

root.dir?, fids-cons(root, fs, ofh), path ∈ root, mode = MODE_R ∨ mode = MODE_RW → pr(user, path, root, fs), mode = MODE_W ∨ mode = MODE_RW → pw(user, path, root, fs) ⊦ root[path].dir?, ∃ n. ¬ n ∈ ofh

User applied rule apply lemma

And obtained the following new goals

Proof step 18:
⊦ ∃ fd. ¬ fd ∈ ofh ∧ (∀ m. ¬ m ∈ ofh → fd ≤ m)
Proof step 19:
root.dir?, fids-cons(root, fs, ofh), path ∈ root, mode = MODE_W ∨ mode = MODE_RW → pw(user, path, root, fs), mode = MODE_R ∨ mode = MODE_RW → pr(user, path, root, fs), ∃ fd. ¬ fd ∈ ofh ∧ (∀ m. ¬ m ∈ ofh → fd ≤ m) ⊦ root[path].dir?, ∃ n. ¬ n ∈ ofh

Rule argument

spec: open-file-handles-ext name: ex-minimal-new-fd seq: ⊦ ∃ fd. ¬ fd ∈ ofh ∧ (∀ m. ¬ m ∈ ofh → fd ≤ m) subst: [ofh] → [ofh]

Additional information

Used terms: ofh