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Proof step 2 from proof notdir-notin (previous step)

⊦ p ∈ tree ↔ p = ε, tree.dir?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ ε ∈ tree
Proof step 4:
⊦ tree.dir? ↔ ¬(∃ fid. tree = fnode(fid))
Proof step 5:
⊦ p ∈ fnode(fid) ↔ p = ε

Rule argument

Additional information

Used simplifier rules: nil-in: ⊦ ε ∈ tree;%fnode-elim-strong: ⊦ tree.dir? ↔ ¬(∃ fid. tree = fnode(fid));%fnode-notin: ⊦ p ∈ fnode(fid) ↔ p = ε;