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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: p ≠ ε ⊦ tree.dir? ∧ parent(p) ∈ tree → tree[p, tree0].dir?; (s)% ⊦ ε ∈ tree; (s)% ⊦ tree[ε, tree0] = tree0; (s)%⊦ pre-mkdir(p, md, ESUCCESS, user, root, fs, ofh) ↔ ¬ p ∈ root ∧ parent(p) ∈ root ∧ root[parent(p)].dir? ∧ py(user, parent(p), root, fs); (s)