[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 85 from proof rename-fids (previous step)

fid ∈ fs ↔ fid ∈ root0.fids ∨ fid ∈ ofh.fids, root0[path'] = fnode(fid1), fnode(fid0) = root0[path], (root0 -- path)[parent(path')].dir?, root0[parent(path')].dir?, fids-cons(root0, fs, ofh), py(user, parent(path), root0, fs), py(user, parent(path'), root0, fs), path' ∈ root0, path ∈ root0, parent(path') ∈ root0 ⊦ fid ∈ fs ↔ fid ∈ ((root0.fids \ {fid0} ) \ (path' ⊑ path ⊃ fnode(fid1) -- restn(# path', path);fnode(fid1)).fids) ∪ {fid0} ∨ fid ∈ ofh.fids, path' = ε, path ⊑ path', ¬ fid1 ∈ ofh.fids ∧ ¬ fid1 ∈ ((root0.fids \ {fid0} ) \ (path' ⊑ path ⊃ fnode(fid1) -- restn(# path', path);fnode(fid1)).fids) ∪ {fid0}

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 86:
⊦ fid ∈ fidb ∪ fidb0 ↔ fid ∈ fidb ∨ fid ∈ fidb0
Proof step 87:
fid ∈ fs ↔ fid ∈ root0.fids ∨ fid ∈ ofh.fids, root0[path'] = fnode(fid1), fnode(fid0) = root0[path], root0[parent(path')].dir?, (root0 -- path)[parent(path')].dir?, fids-cons(root0, fs, ofh), py(user, parent(path'), root0, fs), py(user, parent(path), root0, fs), parent(path') ∈ root0, path ∈ root0, path' ∈ root0 ⊦ fid ∈ fs ↔ (fid ∈ (root0.fids \ {fid0} ) \ (path' ⊑ path ⊃ fnode(fid1) -- restn(# path', path);fnode(fid1)).fids ∨ fid ∈ {fid0} ) ∨ fid ∈ ofh.fids, path' = ε, path ⊑ path', ¬ fid1 ∈ ofh.fids ∧ ¬ fid1 ∈ ((root0.fids \ {fid0} ) \ (path' ⊑ path ⊃ fnode(fid1) -- restn(# path', path);fnode(fid1)).fids) ∪ {fid0}

Rule argument

spec: bag-union, inst: fidbag name: in-union seq: ⊦ fid ∈ fidb ∪ fidb0 ↔ fid ∈ fidb ∨ fid ∈ fidb0 subst: [fidb0, fidb, fid] → [{fid0} , (root0.fids \ {fid0} ) \ (path' ⊑ path ⊃ fnode(fid1) -- restn(# path', path) ;fnode(fid1) ) .fids, fid] flags: <all paths>

Additional information

Used terms: {fid0} , (root0.fids \ {fid0} ) \ (path' ⊑ path ⊃ fnode(fid1) -- restn(# path', path);fnode(fid1)) .fids, fid