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Proof step 1 from proof new-exists (conclusion)

⊦ ∃ ino. ino ≠ 0 ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files

User applied rule apply lemma

And obtained the following new goals

Proof step 2:
⊦ ∃ ino. ino ≠ 0 ∧ (∀ n. n ∈ dirs ∨ n ∈ files → n < ino)
Proof step 3:
∃ ino. ino ≠ 0 ∧ (∀ n. n ∈ dirs ∨ n ∈ files → n < ino) ⊦ ∃ ino. ino ≠ 0 ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files

Rule argument

spec: <toplevel> name: max-exists seq: ⊦ ∃ ino. ino ≠ 0 ∧ (∀ n. n ∈ dirs ∨ n ∈ files → n < ino) subst: [dirs, files] → [dirs, files]

Additional information

Used terms: dirs, files