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Proof step 8 from proof inv-writemeta (previous step)

err = ESUCCESS, err0 = err1, root.dir?, root[path].dir?, fids-cons(root, fs, ofh), pre-writemeta(path, md, err, user, root, fs, ofh) ⊦ ⟪psynced := ?⟫ (root[path, root[path].meta:= md].dir? ∧ fids-cons(root[path, root[path].meta:= md], fs, ofh))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
root[path].dir?, root.dir?, fids-cons(root, fs, ofh), pw(user, path, root, fs), path ∈ root ⊦ ⟪psynced := ?⟫ fids-cons(root[path, dnode(md, root[path].entries)], fs, ofh)

Rule argument

Additional information

Used simplifier rules: ⊦ tree.dir? ∧ p ∈ tree → tree[p, dnode(md, sdt)].dir?; (ss)% ⊦ tree.dir? → tree.meta:= md = dnode(md, tree.entries); (s)%⊦ pre-writemeta(p, md, ESUCCESS, user, root, fs, ofh) ↔ p ∈ root ∧ pw(user, p, root, fs); (s)