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Proof step 47 from proof in-put (previous step)

sdt0[str0][p0] = dnode(md, sdt), p0 ∈ sdt0[str0], str0 ∈ 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))) ⊦ str1 ' ∈ dnode(md0, sdt0[str0, sdt0[str0][p0, dnode(md, sdt[str, tree0])]]) ∧ q0 ∈ dnode(md0, sdt0)[str0 ' + p0, dnode(md, sdt[str, tree0])][str1 '] ↔ ((str0 ' + p0) + str ' ⊑ str1 ' + q0 ⊃ restn(# p0, q0.tail) ∈ tree0;str1 ∈ sdt0 ∧ q0 ∈ sdt0[str1]), p0 = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
⊦ str ' ∈ dnode(md, sdt) ↔ str ∈ sdt
Proof step 49:
p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]])
Proof step 50:
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))) ⊦ str1 ∈ sdt0[str0, sdt0[str0][p0, dnode(md, sdt[str, tree0])]] ∧ q0 ∈ dnode(md0, sdt0[str0, sdt0[str0][p0, dnode(md, sdt[str, tree0])]])[str1 '] ↔ ((str0 ' + p0) + str ' ⊑ str1 ' + q0 ⊃ restn(# p0, q0.tail) ∈ tree0;str1 ∈ sdt0 ∧ q0 ∈ sdt0[str1]), p0 = ε

Rule argument

Additional information

Used simplifier rules: one-ind: ⊦ str ' ∈ dnode(md, sdt) ↔ str ∈ sdt;%put-rec: p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]]);%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]