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Proof step 71 from proof at-put (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 72:
p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]])
Proof step 73:
⊦ str ' ∈ dnode(md, sdt) ↔ str ∈ sdt
Proof step 74:
sdt0[str0][p0] = dnode(md, sdt), str0 ∈ sdt0, p0 ∈ sdt0[str0], 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 '], ∀ 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])] → dnode(md0, sdt0)[p0, dnode(md, sdt[str, tree0])][q] = (p0 + str ' ⊑ q ⊃ tree0[restn(# p0, q.tail)];(q ⊑ p0 ⊃ dnode(md0, sdt0)[q][restn(# q, p0) + str ', tree0];dnode(md0, sdt0)[q])) ⊦ dnode(md0, sdt0[str0, sdt0[str0][p0, dnode(md, sdt[str, tree0])]])[str1 '][q0] = ((str0 ' + p0) + str ' ⊑ str1 ' + q0 ⊃ tree0[restn(# p0, q0.tail)] ;(str1 ' + q0 ⊑ str0 ' + p0 ⊃ dnode(md0, sdt0)[str1 ' + q0][restn(# q0, p0) + str ', tree0];dnode(md0, sdt0)[str1 ' + q0]) ), p0 = ε

Rule argument

Additional information

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