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Proof step 19 from proof fids-put1 (previous step)

tree[parent(p0)].dir?, p0 ∈ tree, tree[parent(p0)].dir? ∧ p0 ∈ tree → tree[p0, tree1].fids = (tree.fids ∪ tree1.fids) \ tree[p0].fids ⊦ dnode(md, sdt0[str, tree])[str ' + p0, tree1].fids = ((sdt0.fids ∪ tree.fids) ∪ tree1.fids) \ tree[p0].fids, p0 = ε, str ∈ sdt0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
tree[p0, tree1].fids = (tree.fids ∪ tree1.fids) \ tree[p0].fids, tree[parent(p0)].dir?, p0 ∈ tree ⊦ dnode(md, sdt0[str, tree])[str ' + p0, tree1].fids = ((sdt0.fids ∪ tree.fids) ∪ tree1.fids) \ tree[p0].fids, p0 = ε, str ∈ sdt0

Proof step 19 from proof fids-put1 (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information