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Proof step 19 from proof at-put (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
⊦ str ' + p ∈ dnode(md, sdt) ↔ str ∈ sdt ∧ p ∈ sdt[str]
Proof step 21:
⊦ str ∈ sdt → dnode(md, sdt)[str ' + p] = sdt[str][p]
Proof step 22:
sdt0[str0][p0] = dnode(md, sdt), str0 ∈ sdt0, p0 ∈ sdt0[str0], q ∈ dnode(md0, sdt0)[str0 ' + p0, dnode(md, sdt[str, tree0])], ∀ 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 ' + p0, dnode(md, sdt[str, tree0])][q] = ((str0 ' + p0) + str ' ⊑ q ⊃ tree0[restn(# p0 + 1, q.tail)] ;(q ⊑ str0 ' + p0 ⊃ dnode(md0, sdt0)[q][restn(# q, str0 ' + p0) + str ', tree0];dnode(md0, sdt0)[q]) )

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)