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Proof step 9 from proof put-fnode (previous step)

dnode(md, sdt)[p, tree0] = fnode(fid), p = str + p0, p ∈ dnode(md, sdt) ⊦ p = ε ∧ tree0 = fnode(fid)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
⊦ str ' + p ∈ dnode(md, sdt) ↔ str ∈ sdt ∧ p ∈ sdt[str]
Proof step 11:
dnode(md, sdt)[str ' + p0, tree0] = fnode(fid), str ∈ sdt, p0 ∈ sdt[str] ⊦

Rule argument

Additional information

Used simplifier rules: in-dnode: ⊦ str ' + p ∈ dnode(md, sdt) ↔ str ∈ sdt ∧ p ∈ sdt[str];% ⊦ str ' + p ≠ ε; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ str + p = str ' + p; (s)