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Proof step 10 from proof inv-writemeta (previous step)

root[path] = dnode(md0, sdt), root.dir?, root[path].dir?, fids-cons(root, fs, ofh), pw(user, path, root, fs), path ∈ root ⊦ ⟪psynced := ?⟫ fids-cons(root[path, dnode(md, sdt)], fs, ofh)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 11:
⊦ fids-cons(tree0, fs0, ofh0) → (fids-cons(tree1, fs1, ofh1) ↔ (∀ fid. (fid ∈ fs0 ↔ fid ∈ tree0.fids ∨ fid ∈ ofh0.fids) → (fid ∈ fs1 ↔ fid ∈ tree1.fids ∨ fid ∈ ofh1.fids)))

Rule argument

Additional information

Used simplifier rules: fids-cons-reduce: ⊦ fids-cons(tree0, fs0, ofh0) → ( fids-cons(tree1, fs1, ofh1) ↔ (∀ fid. (fid ∈ fs0 ↔ fid ∈ tree0.fids ∨ fid ∈ ofh0.fids) → (fid ∈ fs1 ↔ fid ∈ tree1.fids ∨ fid ∈ ofh1.fids)));%⊦ p ∈ tree ∧ tree[p] = dnode(md0, sdt) → tree[p, dnode(md1, sdt)].fids = tree.fids; (s)