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Proof step 52 from proof at-mod (previous step)

sdt[str][p0] = dnode(md0, sdt0), q0 ∈ sdt[str, sdt[str][p0, dnode(md1, sdt1)]][str0], p0 ∈ sdt[str], str ∈ sdt, str0 ∈ sdt[str, sdt[str][p0, dnode(md1, sdt1)]], ∀ md, sdt, md0, sdt0, q, md1, sdt1. dnode(md, sdt)[p0] = dnode(md0, sdt0) ∧ p0 ∈ dnode(md, sdt) ∧ q ∈ dnode(md, sdt)[p0, dnode(md1, sdt1)] → dnode(md, sdt)[p0, dnode(md1, sdt1)][q] = (q ⊑ p0 ⊃ dnode(md, sdt)[q][restn(# q, p0), dnode(md1, sdt1)];dnode(md, sdt)[p0, dnode(md0, sdt1)][q]) ⊦ dnode(md, sdt[str, sdt[str][p0, dnode(md1, sdt1)]])[str0 '][q0] = (str0 ' + q0 ⊑ str ' + p0 ⊃ dnode(md, sdt)[str0 ' + q0][restn(# q0, p0), dnode(md1, sdt1)] ;dnode(md, sdt[str, sdt[str][p0, dnode(md0, sdt1)]])[str0 ' + q0] ), p0 = ε

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, sdt[str][p0, dnode(md1, sdt1)], str, sdt] flags: <all paths>

Additional information

Used terms: str0, sdt[str][p0, dnode(md1, sdt1)], str, sdt