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Proof step 1 from proof expath-rec (conclusion)

⊦ ispath(str ' + q, n, dirs, files) ↔ valid-dir-ino(n, dirs, files) ∧ str ∈ dirs[n].entries ∧ ispath(q, dirs[n].entries[str], dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ ispath(str ' + q, n, dirs, files) ↔ n ∈ dirs ∧ str ∈ dirs[n].entries ∧ ispath(q, dirs[n].entries[str], dirs, files)

Rule argument

Additional information

Used simplifier rules: valid-dir-ino: ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs;