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Proof step 1 from proof fids-strpath (conclusion)

⊦ fid ∈ sdt.fids ↔ (∃ str, p. str ∈ sdt ∧ p ∈ sdt[str] ∧ sdt[str][p] = fnode(fid))

User applied rule induction

And obtained the following new goals

Proof step 2:
∀ sdt0, fid. # sdt0 < # sdt → true → (fid ∈ sdt0.fids ↔ (∃ str, p. str ∈ sdt0 ∧ p ∈ sdt0[str] ∧ sdt0[str][p] = fnode(fid))) ⊦ fid ∈ sdt.fids ↔ (∃ str, p. str ∈ sdt ∧ p ∈ sdt[str] ∧ sdt[str][p] = fnode(fid))

Rule argument

indvar: # sdt wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # sdt