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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ tree.dir? ↔ ¬(∃ fid. tree = fnode(fid))
Proof step 4:
⊦ fnode(fid).fid:= fid0 = fnode(fid0)

Rule argument

Additional information

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