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Proof step 7 from proof dir-put3 (previous step)

dnode(md, sdt)[str ' + p0, tree0] = fnode(fid), parent(str ' + p0) ∈ dnode(md, sdt) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: put-rec seq: p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]]) subst: [tree0, p, str, sdt, md] → [tree0, p0, str, sdt, md] flags: <all paths>

Additional information

Used simplifier rules: in-dnode: ⊦ str ' + p ∈ dnode(md, sdt) ↔ str ∈ sdt ∧ p ∈ sdt[str];%put-rec: p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]]);%put-here: ⊦ dnode(md, sdt)[str ', tree0] = dnode(md, sdt[str, tree0]);% ⊦ fnode(fid) ≠ dnode(md, sdt); (s)% ⊦ p ≠ ε → parent(str ' + p) = str ' + parent(p); (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p + ε = p; (s) Used terms: tree0, p0, str, sdt, md