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Proof step 9 from proof at-mod (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 10:
⊦ tree[ε] = tree
Proof step 11:
q ∈ dnode(md1, sdt1) ⊦ dnode(md1, sdt1)[q] = dnode(md0, sdt1)[q], q = ε

Rule argument

pos: right 1

Additional information

Used simplifier rules: nil-at: ⊦ tree[ε] = tree;