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Proof step 7 from proof new-exists (previous step)

ino ∈ dirs, ∀ n. n ∈ dirs ∨ n ∈ files → n < ino ⊦ ino = 0, ∃ ino. ino ≠ 0 ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
ino ∈ dirs, ∀ n. n ∈ dirs ∨ n ∈ files → n < ino ⊦ ∃ ino. ino ≠ 0 ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ dirs → ino ≠ 0; (s)