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Proof step 32 from proof fids-in (previous step)

tree[p] = fnode(fid), p ∈ tree ⊦ fid ∈ tree.fids

User applied rule structural induction

And obtained the following new goals

Proof step 33:
⊦ fnode(fid).fids = {fid}
Proof step 34:
tree[str + p0] = fnode(fid), str + p0 ∈ tree, ∀ tree, fid. tree[p0] = fnode(fid) ∧ p0 ∈ tree → fid ∈ tree.fids ⊦ fid ∈ tree.fids

Rule argument

indvar: p

Additional information

Used simplifier rules: fids-fnode: ⊦ fnode(fid).fids = {fid} ;%path freely generated by ε, +;;% ⊦ tree[ε] = tree; (s)% ⊦ ε ∈ tree; (s)% ⊦ fid ∈ {fid0} ↔ fid = fid0; (s)