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Proof step 16 from proof inv-create (previous step)

fid0 ∈ fs ↔ fid0 ∈ root.fids ∨ fid0 ∈ ofh.fids, root[parent(path)].dir?, root.dir?, fids-cons(root, fs, ofh), py(user, parent(path), root, fs), parent(path) ∈ root ⊦ fid0 ∈ fs[fid, mkfile(md, mkbuf(0))] ↔ (fid0 ∈ root.fids ∨ fid0 ∈ {fid} ) ∨ fid0 ∈ ofh.fids, fid ∈ fs, path ∈ root

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
fid0 ∈ fs ↔ fid0 ∈ root.fids ∨ fid0 ∈ ofh.fids, root.dir?, root[parent(path)].dir?, fids-cons(root, fs, ofh), py(user, parent(path), root, fs), parent(path) ∈ root ⊦ fid0 ∈ fs[fid, mkfile(md, mkbuf(0))] ↔ fid0 ∈ root.fids ∨ fid0 = fid ∨ fid0 ∈ ofh.fids, path ∈ root, fid ∈ fs

Rule argument

Additional information

Used simplifier rules: ⊦ fid ∈ {fid0} ↔ fid = fid0; (s)