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Proof step 35 from proof at-mod (previous step)

sdt[str] = dnode(md0, sdt0), str0 = str, str0 ∈ sdt[str, dnode(md1, sdt1)], str ∈ sdt, q0 ∈ sdt[str, dnode(md1, sdt1)][str0], ∀ md2, sdt2, md3, sdt3, q, md4, sdt4. dnode(md2, sdt2) = dnode(md3, sdt3) ∧ q ∈ dnode(md4, sdt4) → dnode(md4, sdt4)[q] = (q = ε ⊃ dnode(md4, sdt4);dnode(md3, sdt4)[q]) ⊦ dnode(md, sdt[str, dnode(md1, sdt1)])[str0 '][q0] = (str0 ' + q0 = str ' ⊃ dnode(md, sdt)[str0 ' + q0][restn(# q0, ε), dnode(md1, sdt1)];dnode(md, sdt[str, dnode(md0, sdt1)])[str0 ' + q0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
str ∈ sdt ⊦ dnode(md, sdt)[str '] = sdt[str]
Proof step 37:
⊦ tree[ε, tree0] = tree0
Proof step 38:
⊦ dnode(md, sdt[str, tree])[str ' + p] = tree[p]
Proof step 39:
sdt[str] = dnode(md0, sdt0), str ∈ sdt, q0 ∈ dnode(md1, sdt1), ∀ md2, sdt2, md3, sdt3, q, md4, sdt4. dnode(md2, sdt2) = dnode(md3, sdt3) ∧ q ∈ dnode(md4, sdt4) → dnode(md4, sdt4)[q] = (q = ε ⊃ dnode(md4, sdt4);dnode(md3, sdt4)[q]) ⊦ dnode(md1, sdt1)[q0] = (q0 = ε ⊃ dnode(md1, sdt1);dnode(md0, sdt1)[q0])

Rule argument

Additional information

Used simplifier rules: one-at: str ∈ sdt ⊦ dnode(md, sdt)[str '] = sdt[str];%nil-put: ⊦ tree[ε, tree0] = tree0;%at-dnode-same: ⊦ dnode(md, sdt[str, tree])[str ' + p] = tree[p];% ⊦ str ∈ sdt[str, tree]; (s)% ⊦ restn(0, p) = p; (s)% ⊦ # ε = 0; (s)% ⊦ p + ε = p; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p = p + p0 ↔ p0 = ε; (s)% ⊦ sdt[str, tree][str] = tree; (s)% ⊦ str ∈ sdt[str0, tree] ↔ str = str0 ∨ str ∈ sdt; (ws)