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Proof step 33 from proof at-mod (previous step)

sdt[str] = dnode(md0, sdt0), q0 ∈ sdt[str, dnode(md1, sdt1)][str0], str ∈ sdt, str0 ∈ sdt[str, dnode(md1, sdt1)], ∀ md2, sdt2, md3, sdt3, q, md4, sdt4. dnode(md2, sdt2) = dnode(md3, sdt3) ∧ q ∈ dnode(md4, sdt4) → dnode(md4, sdt4)[q] = (q = ε ⊃ dnode(md4, sdt4);dnode(md3, sdt4)[q]) ⊦ dnode(md, sdt[str, dnode(md1, sdt1)])[str0 '][q0] = (str0 ' + q0 = str ' ⊃ dnode(md, sdt)[str0 ' + q0][restn(# q0, ε), dnode(md1, sdt1)];dnode(md, sdt[str, dnode(md0, sdt1)])[str0 ' + q0])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: directory-tree-inst name: At-other seq: ⊦ str ≠ str0 → sdt[str0, tree][str] = sdt[str] subst: [str, tree, str0, sdt] → [str0, dnode(md1, sdt1), str, sdt] flags: <all paths>

Additional information

Used terms: str0, dnode(md1, sdt1), str, sdt