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Proof step 4 from proof C-ext (previous step)

∀ str. (str ∈ entries ↔ dentrykey(ino, str) ∈ ri) ∧ (str ∈ entries → entries[str] = fs[ri[dentrykey(ino, str)]].ino) ⊦ ∀ str. (str ∈ entries ↔ str ∈ abs-children(ino, fs, ri)) ∧ (str ∈ entries → entries[str] = abs-children(ino, fs, ri)[str])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: in-children: ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri;