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Proof step 11 from proof plinksd+ (previous step)

p ∈ links(fid, dnode(md, sdt[str, tree])) ⊦ str ∈ sdt, p ∈ links(fid, dnode(md, sdt)), p ≠ ε ∧ p.head = str ∧ p.tail ∈ links(fid, tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
⊦ p ∈ links(fid, tree) ↔ p ∈ tree ∧ tree[p] = fnode(fid)
Proof step 13:
dnode(md, sdt[str, tree])[p] = fnode(fid), p ∈ dnode(md, sdt[str, tree]) ⊦ p = ε, str ∈ sdt, p ∈ links(fid, dnode(md, sdt)), p.tail ∈ links(fid, tree) ∧ p.head = str

Rule argument

Additional information

Used simplifier rules: in-plinks: ⊦ p ∈ links(fid, tree) ↔ p ∈ tree ∧ tree[p] = fnode(fid);% ⊦ fnode(fid) ≠ dnode(md, sdt); (s)% ⊦ tree[ε] = tree; (s)