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

p ∈ tree ⊦ tree[p, tree0] = fnode(fid) ↔ p = ε ∧ tree0 = fnode(fid)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ tree[ε, tree0] = tree0
Proof step 4:
tree[p, tree0] = fnode(fid), p ∈ tree ⊦ p = ε ∧ tree0 = fnode(fid)

Rule argument

Additional information

Used simplifier rules: nil-put: ⊦ tree[ε, tree0] = tree0;% ⊦ fnode(fid) = fnode(fid0) ↔ fid = fid0; (s)