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Proof step 15 from proof in-put (previous step)

dnode(md0, sdt0)[str0 + p0] = dnode(md, sdt), str0 + p0 ∈ dnode(md0, sdt0), ∀ md0, sdt0, md, sdt, q, str, tree0. dnode(md0, sdt0)[p0] = dnode(md, sdt) ∧ p0 ∈ dnode(md0, sdt0) → (q ∈ dnode(md0, sdt0)[p0, dnode(md, sdt[str, tree0])] ↔ (p0 + str ' ⊑ q ⊃ restn(# p0, q.tail) ∈ tree0;q ∈ dnode(md0, sdt0))) ⊦ q ∈ dnode(md0, sdt0)[str0 + p0, dnode(md, sdt[str, tree0])] ↔ ((str0 + p0) + str ' ⊑ q ⊃ restn(#(str0 + p0), q.tail) ∈ tree0;q ∈ dnode(md0, sdt0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
⊦ str ' + p ∈ dnode(md, sdt) ↔ str ∈ sdt ∧ p ∈ sdt[str]
Proof step 17:
⊦ str ∈ sdt → dnode(md, sdt)[str ' + p] = sdt[str][p]
Proof step 18:
sdt0[str0][p0] = dnode(md, sdt), str0 ∈ sdt0, p0 ∈ sdt0[str0], ∀ md0, sdt0, md, sdt, q, str, tree0. dnode(md0, sdt0)[p0] = dnode(md, sdt) ∧ p0 ∈ dnode(md0, sdt0) → (q ∈ dnode(md0, sdt0)[p0, dnode(md, sdt[str, tree0])] ↔ (p0 + str ' ⊑ q ⊃ restn(# p0, q.tail) ∈ tree0;q ∈ dnode(md0, sdt0))) ⊦ q ∈ dnode(md0, sdt0)[str0 ' + p0, dnode(md, sdt[str, tree0])] ↔ ((str0 ' + p0) + str ' ⊑ q ⊃ restn(# p0 + 1, q.tail) ∈ tree0;q ∈ dnode(md0, sdt0))

Rule argument

Additional information

Used simplifier rules: in-dnode: ⊦ str ' + p ∈ dnode(md, sdt) ↔ str ∈ sdt ∧ p ∈ sdt[str];%at-dnode: ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p] = sdt[str][p];% ⊦ m +1 = m + 1; (s)% ⊦ #(str ' + p) = (# p)+1; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ str + p = str ' + p; (s)