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Proof step 29 from proof ubifs-cons-reduce (previous step)

fs1[ri1[key]].key = key, ro1.inodes?, fo1.inodes?, log-cons(log1, fs1), ubifs-cons(fs0, ri0, ro0, fi0, fo0, log0), ri1[key] ∈ fs1, key ∈ ri1, ro1 ⊆ dom ri1, fo1 ⊆ dom fi1, inodekey(key.ino) ∈ ri1 → ri1[inodekey(key.ino)] ∈ fs1 ∧ node-closed(fs1[ri1[inodekey(key.ino)]], ri1, fs1, ro1), fs1[ri1[key]].data? → inodekey(key.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE, fs1[ri1[key]].dentry? → inodekey(key.ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro1 ∧ fs1[ri1[inodekey(key.ino)]].directory ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro1, key ∈ ri0 → ri0[key] ∈ fs0 ∧ fs0[ri0[key]].key = key ∧ (key.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro0 ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro0 ∧ fs0[ri0[inodekey(key.ino)]].directory) ∧ (key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE), key.inode? → fs1[ri1[key]].inode? ∧ key.ino ≠ 0, key.dentry? → fs1[ri1[key]].dentry?, key.data? → fs1[ri1[key]].data?, inodekey(fs1[ri1[key]].ino) ∈ ri1 → ri1[inodekey(fs1[ri1[key]].ino)] ∈ fs1 ∧ node-closed(fs1[ri1[inodekey(fs1[ri1[key]].ino)]], ri1, fs1, ro1), inodekey(key.ino) ∈ ri1 → ri1[inodekey(key.ino)] ∈ fs1 ∧ fs1[ri1[inodekey(key.ino)]].inode? ∧ fs1[ri1[inodekey(key.ino)]].key = inodekey(key.ino) ∧ key.ino ≠ 0, inodekey(fs1[ri1[key]].ino) ∈ ri1 → ri1[inodekey(fs1[ri1[key]].ino)] ∈ fs1 ∧ fs1[ri1[inodekey(fs1[ri1[key]].ino)]].inode? ∧ fs1[ri1[inodekey(fs1[ri1[key]].ino)]].key = inodekey(fs1[ri1[key]].ino) ∧ fs1[ri1[key]].ino ≠ 0, ∀ key. key ∈ ri1 → ri1[key] ∈ fs1 ∧ key-cons(key, fs1[ri1[key]]), ∀ key. key ∈ ri1 → ri1[key] ∈ fs1 ∧ node-closed(fs1[ri1[key]], ri1, fs1, ro1) ⊦ dups(log1), inodekey(0) ∈ ri1, ( key.dentry? → fs1[ri1[key]].dentry? ∧ inodekey(key.ino) ∈ ri1 ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro1 ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro1 ∧ fs1[ri1[inodekey(key.ino)]].directory) ∧ (key.data? → fs1[ri1[key]].data? ∧ inodekey(key.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE)

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 3

Additional information

Used simplifier rules: elim-dentry: ⊦ key.dentry? ↔ (∃ ino, str. key = dentrykey(ino, str));%elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ ¬ datakey(m, m0).dentry?; (s)% ⊦ ¬ datakey(m, m0).inode?; (s)% ⊦ dentrykey(m, str).ino = m; (s)% ⊦ ¬ dentrykey(m, str).data?; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ ¬ dentrykey(m, str).inode?; (s)