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Proof step 63 from proof at-put (previous step)

sdt0[str0] = dnode(md, sdt), str1 ∈ sdt0[str0, dnode(md, sdt[str, tree0])], str0 ∈ sdt0, q0 ∈ sdt0[str0, dnode(md, sdt[str, tree0])][str1], ∀ md1, sdt1, md2, sdt2, q, str2, tree. dnode(md1, sdt1) = dnode(md2, sdt2) ∧ q ∈ dnode(md2, sdt2[str2, tree]) → dnode(md2, sdt2[str2, tree])[q] = (str2 ' ⊑ q ⊃ tree[q.tail];(q = ε ⊃ dnode(md1, sdt1[str2, tree]);dnode(md1, sdt1)[q])) ⊦ str1 ' + q0 = str0 ', dnode(md0, sdt0[str0, dnode(md, sdt[str, tree0])])[str1 '][q0] = dnode(md0, sdt0)[str1 ' + q0], str0 ' + str ' ⊑ str1 ' + 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] → [str1, dnode(md, sdt[str, tree0]), str0, sdt0] flags: <all paths>

Additional information

Used simplifier rules: one-at: str ∈ sdt ⊦ dnode(md, sdt)[str '] = sdt[str];%at-dnode: ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p] = sdt[str][p];% ⊦ str ∈ sdt[str0, tree] ↔ str = str0 ∨ str ∈ sdt; (ws)% ⊦ str ≠ str0 → (str ∈ sdt[str0, tree] ↔ str ∈ sdt); (s)% ⊦ str ≠ str0 → sdt[str0, tree][str] = sdt[str]; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path] Used terms: str1, dnode(md, sdt[str, tree0]), str0, sdt0