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Proof step 12 from proof at-mod (previous step)

q ∈ dnode(md1, sdt1) ⊦ dnode(md1, sdt1)[q] = dnode(md0, sdt1)[q], q = ε

User applied rule constructor cut

And obtained the following new goals

Proof step 13:
⊦ str ' + p ∈ dnode(md, sdt) ↔ str ∈ sdt ∧ p ∈ sdt[str]
Proof step 14:
⊦ str ∈ sdt → dnode(md, sdt)[str ' + p] = sdt[str][p]

Rule argument

var: q

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];%path freely generated by ε, +;;% ⊦ str + p = str ' + p; (s)% ⊦ str ' + p ≠ ε; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]