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Proof step 60 from proof at-put (previous step)

sdt0[str0] = dnode(md, sdt), str0 ∈ sdt0, q0 ∈ dnode(md0, sdt0[str0, dnode(md, sdt[str, tree0])])[str1 '], str1 ∈ sdt0[str0, dnode(md, sdt[str, tree0])], ∀ md1, sdt1, md2, sdt2, q, str2, tree. dnode(md1, sdt1) = dnode(md2, sdt2) ∧ q ∈ dnode(md2, sdt2[str2, tree]) → dnode(md2, sdt2[str2, tree])[q] = (str2 ' ⊑ q ⊃ tree[q.tail];(q = ε ⊃ dnode(md1, sdt1[str2, tree]);dnode(md1, sdt1)[q])) ⊦ str1 ' + q0 = str0 ', dnode(md0, sdt0[str0, dnode(md, sdt[str, tree0])])[str1 '][q0] = dnode(md0, sdt0)[str1 ' + q0], str0 ' + str ' ⊑ str1 ' + q0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 61:
str ∈ sdt ⊦ dnode(md, sdt)[str '] = sdt[str]
Proof step 62:
sdt0[str0] = dnode(md, sdt), q0 ∈ sdt0[str0, dnode(md, sdt[str, tree0])][str1], str0 ∈ sdt0, str1 ∈ sdt0[str0, dnode(md, sdt[str, tree0])], ∀ md1, sdt1, md2, sdt2, q, str2, tree. dnode(md1, sdt1) = dnode(md2, sdt2) ∧ q ∈ dnode(md2, sdt2[str2, tree]) → dnode(md2, sdt2[str2, tree])[q] = (str2 ' ⊑ q ⊃ tree[q.tail];(q = ε ⊃ dnode(md1, sdt1[str2, tree]);dnode(md1, sdt1)[q])) ⊦ str1 ' + q0 = str0 ', dnode(md0, sdt0[str0, dnode(md, sdt[str, tree0])])[str1 '][q0] = dnode(md0, sdt0)[str1 ' + q0], str0 ' + str ' ⊑ str1 ' + q0

Rule argument

spec: <toplevel> name: one-at seq: str ∈ sdt ⊦ dnode(md, sdt)[str '] = sdt[str] subst: [str, sdt, md] → [str1, sdt0[str0, dnode(md, sdt[str, tree0])], md0] flags: <all paths>

Additional information

Used terms: str1, sdt0[str0, dnode(md, sdt[str, tree0])], md0