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Proof step 22 from proof at-put (previous step)

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]) )

User applied rule constructor cut

And obtained the following new goals

Proof step 23:
sdt0[str0][p0] = dnode(md, sdt), q = ε, q ∈ 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 ' + 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]) )
Proof step 34:
sdt0[str0][p0] = dnode(md, sdt), q = str1 + q0, q ∈ 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 ' + 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

var: q

Additional information

Used simplifier rules: path freely generated by ε, +;;