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Proof step 15 from proof inv-close (previous step)

fid0 ∈ fs ↔ fid0 ∈ root.fids ∨ fid0 ∈ ofh0.fids, 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 ∈ root.fids, fid ∈ (ofh0 -- fd).fids

User applied rule case distinction

And obtained the following new goals

Proof step 16:
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
Proof step 22:
ofh0[fd] = mkfh(fid, mode, m), root.dir?, fids-cons(root, fs, ofh0), fd ∈ ofh0, fid0 ∈ fs, fid0 ∈ root.fids ∨ fid0 ∈ ofh0.fids ⊦ fid0 ≠ fid ∧ fid0 ∈ fs ↔ fid0 ∈ root.fids ∨ fid0 ∈ (ofh0 -- fd).fids, fid ∈ (ofh0 -- fd).fids, fid ∈ root.fids

Rule argument

pos: left 1

Proof step 15 from proof inv-close (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information