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Proof step 30 from proof in-mod (previous step)

sdt0[str][p0] = dnode(md0, sdt), p0 ∈ sdt0[str], str ∈ sdt0, ∀ md, sdt0, md0, sdt, q, md1. dnode(md, sdt0)[p0] = dnode(md0, sdt) ∧ p0 ∈ dnode(md, sdt0) → (q ∈ dnode(md, sdt0)[p0, dnode(md1, sdt)] ↔ q ∈ dnode(md, sdt0)) ∨ p0 = ε ⊦ str0 ' ∈ dnode(md, sdt0[str, sdt0[str][p0, dnode(md1, sdt)]]) ∧ q0 ∈ dnode(md, sdt0)[str ' + p0, dnode(md1, sdt)][str0 '] ↔ str0 ∈ sdt0 ∧ q0 ∈ sdt0[str0], p0 = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
⊦ str ' ∈ dnode(md, sdt) ↔ str ∈ sdt
Proof step 32:
p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]])
Proof step 33:
sdt0[str][p0] = dnode(md0, sdt), str ∈ sdt0, p0 ∈ sdt0[str], ∀ md2, sdt1, md3, sdt2, q, md4. dnode(md2, sdt1)[p0] = dnode(md3, sdt2) ∧ p0 ∈ dnode(md2, sdt1) → (q ∈ dnode(md2, sdt1)[p0, dnode(md4, sdt2)] ↔ q ∈ dnode(md2, sdt1)) ⊦ str0 ∈ sdt0[str, sdt0[str][p0, dnode(md1, sdt)]] ∧ q0 ∈ dnode(md, sdt0[str, sdt0[str][p0, dnode(md1, sdt)]])[str0 '] ↔ str0 ∈ sdt0 ∧ q0 ∈ sdt0[str0], 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]