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Proof step 8 from proof ubifs-cons-pagesize (previous step)

key.data?, fo.inodes?, ro.inodes?, log-cons(log, fs), node-closed(fs[ri[key]], ri, fs, ro), ri-cons(ri, fs), key ∈ ri, ri[key] ∈ fs, fo ⊆ dom fi, ro ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro) ⊦ # fs[ri[key]].data = VFS_PAGE_SIZE, dups(log), inodekey(0) ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ node-closed(nd, ri, fs, ro) ↔ ( nd.dentry? → inodekey(nd.key.ino) ∈ ri ∧ ¬ inodekey(nd.key.ino) ∈ ro ∧ fs[ri[inodekey(nd.key.ino)]].directory ∧ inodekey(nd.ino) ∈ ri ∧ ¬ inodekey(nd.ino) ∈ ro) ∧ (nd.data? → inodekey(nd.key.ino) ∈ ri ∧ ¬ fs[ri[inodekey(nd.key.ino)]].directory ∧ # nd.data = VFS_PAGE_SIZE)
Proof step 10:
key.data?, ro.inodes?, fo.inodes?, log-cons(log, fs), ri-cons(ri, fs), ri[key] ∈ fs, key ∈ ri, ro ⊆ dom ri, fo ⊆ dom fi, fs[ri[key]].dentry? → inodekey(fs[ri[key]].key.ino) ∈ ri ∧ ¬ inodekey(fs[ri[key]].key.ino) ∈ ro ∧ fs[ri[inodekey(fs[ri[key]].key.ino)]].directory ∧ inodekey(fs[ri[key]].ino) ∈ ri ∧ ¬ inodekey(fs[ri[key]].ino) ∈ ro, fs[ri[key]].data? → inodekey(fs[ri[key]].key.ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[key]].key.ino)]].directory ∧ # fs[ri[key]].data = VFS_PAGE_SIZE, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro) ⊦ # fs[ri[key]].data = VFS_PAGE_SIZE, dups(log), inodekey(0) ∈ ri

Rule argument

spec: aubifs-inv name: node-closed seq: ⊦ node-closed(nd, ri, fs, ro) ↔ ( nd.dentry? → inodekey(nd.key.ino) ∈ ri ∧ ¬ inodekey(nd.key.ino) ∈ ro ∧ fs[ri[inodekey(nd.key.ino)]].directory ∧ inodekey(nd.ino) ∈ ri ∧ ¬ inodekey(nd.ino) ∈ ro) ∧ ( nd.data? → inodekey(nd.key.ino) ∈ ri ∧ ¬ fs[ri[inodekey(nd.key.ino)]].directory ∧ # nd.data = VFS_PAGE_SIZE) subst: [ro, fs, ri, nd] → [ro, fs, ri, fs[ri[key]]] flags: <all paths>

Additional information

Used terms: ro, fs, ri, fs[ri[key]]