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

ofh0[fd] = mkfh(fid, mode, m), root.dir?, fids-cons(root, fs, ofh0), fd ∈ ofh0 ⊦ fid0 ≠ fid ∧ fid0 ∈ fs ↔ fid0 ∈ root.fids ∨ fid0 ∈ (ofh0 -- fd).fids, fid ∈ (ofh0 -- fd).fids, fid ∈ root.fids, fid0 ∈ root.fids, fid0 ∈ ofh0.fids, fid0 ∈ fs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
ofh0[fd] = mkfh(fid, mode, m), root.dir?, fids-cons(root, fs, ofh0), fid0 ∈ (ofh0 -- fd).fids, fd ∈ ofh0 ⊦ # (ofh0 -- fd).fids = 0, (ofh0 -- fd).fids = ∅, fid ∈ (ofh0 -- fd).fids, fid ∈ root.fids, fid0 ∈ root.fids, fid0 ∈ ofh0.fids, fid0 ∈ fs

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ fids ≠ ∅ → # fids ≠ 0; (forward) from specification set-basic[fidset]%ne-01: ⊦ fid ∈ fids → fids ≠ ∅; (forward) from specification set-basic[fidset]