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Proof step 11 from proof subdirs-add-entry (previous step)

ino ∈ dirs, str ∈ entries, entries[str] ∈ dirs, str0 ∈ entries[str, ino0], entries[str, ino0][str0] ∈ dirs ⊦ ino0 ∈ dirs, str0 ≠ str ∧ str0 ∈ entries ∧ entries[str0] ∈ dirs

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: str0 = str

Additional information

Used simplifier rules: ⊦ str ≠ str0 → (str ∈ entries[str0, ino] ↔ str ∈ entries); (s)% ⊦ str ≠ str0 → entries[str0, ino][str] = entries[str]; (s)% ⊦ str ∈ entries[str, ino]; (s)% ⊦ entries[str, ino][str] = ino; (s) Used formulas: str0 = str