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Proof step 36 from proof links-add-entry (previous step)

p_ino ∈ dirs, str ∈ entries1 ⊦ str0 ∈ entries1[str, ino] ∧ ino0 = entries1[str, ino][str0] ↔ str0 ∈ entries1 ∧ ino0 = entries1[str0], entries1[str] = ino0, ino = ino0

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