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Proof step 5 from proof fids-strpath (previous step)

∀ 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)), sdt = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: directory-tree-inst name: exnotempty seq: ⊦ sdt = ∅ ↔ ¬(∃ str, tree, sdt0. sdt = sdt0[str, tree] ∧ ¬ str ∈ sdt0) subst: [sdt] → [sdt] flags: <all paths>

Additional information

Used terms: sdt