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Proof step 2 from proof dir-elimput (previous step)

tree.dir? ⊦ tree[str ', tree0] = dnode(tree.meta, tree.entries[str, tree0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ tree.dir? ↔ (∃ md, sdt. tree = dnode(md, sdt))
Proof step 4:
⊦ dnode(md, sdt)[str ', tree0] = dnode(md, sdt[str, tree0])
Proof step 5:
⊦ dnode(md, sdt).meta = md
Proof step 6:
⊦ dnode(md, sdt).entries = sdt

Rule argument

Additional information

Used simplifier rules: dnode-elim-strong: ⊦ tree.dir? ↔ (∃ md, sdt. tree = dnode(md, sdt));%put-here: ⊦ dnode(md, sdt)[str ', tree0] = dnode(md, sdt[str, tree0]);%meta: ⊦ dnode(md, sdt).meta = md;%entries: ⊦ dnode(md, sdt).entries = sdt;