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Proof step 2 from proof fnode-elim (previous step)

⊦ fid = tree.fid ↔ tree = fnode(fid), tree.dir?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: fid: ⊦ fnode(fid).fid = fid;%fnode-elim-strong: ⊦ tree.dir? ↔ ¬(∃ fid. tree = fnode(fid));% ⊦ fnode(fid) = fnode(fid0) ↔ fid = fid0; (s)