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Proof step 2 from proof read-notin (previous step)

⊦ sdt[str] = (∅)[str], str ∈ sdt

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ str. sdt0[str] = (∅)[str] ∨ str ∈ sdt0 ⊦ sdt0[str0, tree][str] = (∅)[str], str ∈ sdt0[str0, tree]

Rule argument

term: sdt

Additional information

Used simplifier rules: directory-tree, entries-tree generated by ∅, dnode, fnode, [ ];;