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Proof step 2 from proof dir-put3 (previous step)

tree.dir?, parent(p) ∈ tree ⊦ p = ε, tree[p, tree0].dir?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ tree.dir? ↔ (∃ md, sdt. tree = dnode(md, sdt))
Proof step 4:
⊦ tree.dir? ↔ ¬(∃ fid. tree = fnode(fid))
Proof step 5:
dnode(md, sdt)[p, tree0] = fnode(fid), parent(p) ∈ dnode(md, sdt) ⊦ p = ε

Rule argument

Additional information

Used simplifier rules: dnode-elim-strong: ⊦ tree.dir? ↔ (∃ md, sdt. tree = dnode(md, sdt));%fnode-elim-strong: ⊦ tree.dir? ↔ ¬(∃ fid. tree = fnode(fid));