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Proof step 14 from proof inv-create (previous step)

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 ∪ {fid} ∨ fid0 ∈ ofh.fids, path ∈ root, fid ∈ fs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ fid ∈ fidb ∪ fidb0 ↔ fid ∈ fidb ∨ fid ∈ fidb0
Proof step 16:
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

Rule argument

spec: bag-union, inst: fidbag name: in-union seq: ⊦ fid ∈ fidb ∪ fidb0 ↔ fid ∈ fidb ∨ fid ∈ fidb0 subst: [fidb0, fidb, fid] → [{fid} , root.fids, fid0] flags: <all paths>

Additional information

Used terms: {fid} , root.fids, fid0