[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

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

fid0 ∈ fs ↔ fid0 ∈ root.fids ∨ fid0 ∈ ofh.fids, root[path] = fnode(fid), root[parent(path')].dir?, root.dir?, fids-cons(root, fs, ofh), px(user, parent(path), root, fs), py(user, parent(path'), root, fs), parent(path') ∈ root, path ∈ root ⊦ fid0 ∈ fs ↔ fid0 ∈ root.fids ∪ {fid} ∨ fid0 ∈ ofh.fids, path' ∈ root

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ fid ∈ fidb ∪ fidb0 ↔ fid ∈ fidb ∨ fid ∈ fidb0
Proof step 17:
fid0 ∈ fs ↔ fid0 ∈ root.fids ∨ fid0 ∈ ofh.fids, root[path] = fnode(fid), root.dir?, root[parent(path')].dir?, fids-cons(root, fs, ofh), px(user, parent(path), root, fs), py(user, parent(path'), root, fs), path ∈ root, parent(path') ∈ root ⊦ fid0 ∈ fs ↔ (fid0 ∈ root.fids ∨ fid0 ∈ {fid} ) ∨ fid0 ∈ ofh.fids, 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