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

err = ESUCCESS, err0 = err1, root.dir?, fids-cons(root, fs, ofh), pre-rmdir(path, err, user, root, fs, ofh) ⊦ (root -- path).dir? ∧ fids-cons(root -- path, fs, ofh)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ 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)))
Proof step 10:
root[path].entries = ∅, fid ∈ fs ↔ fid ∈ root.fids ∨ fid ∈ ofh.fids, root.dir?, root[path].dir?, fids-cons(root, fs, ofh), py(user, parent(path), root, fs), path ∈ root ⊦ fid ∈ fs ↔ fid ∈ root.fids \ root[path].fids ∨ fid ∈ ofh.fids, path = ε

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 ≠ ε ⊦ p ∈ tree → (tree -- p).fids = tree.fids \ tree[p].fids; (s)%p ≠ ε ⊦ p ∈ tree → ((tree -- p).dir? ↔ tree.dir?); (s)%⊦ pre-rmdir(p, ESUCCESS, user, root, fs, ofh) ↔ p ≠ ε ∧ p ∈ root ∧ root[p].dir? ∧ root[p].entries = ∅ ∧ py(user, parent(p), root, fs); (s)