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Proof step 118 from proof ubifs-cons-reduce (previous step)

fs0[ri0[datakey(ino, n)]].key = datakey(ino, n), fs0[ri0[datakey(ino, n)]].data?, ro0.inodes?, fo0.inodes?, log-cons(log0, fs0), log-cons(log1, fs1), node-closed(fs0[ri0[datakey(ino, n)]], ri0, fs0, ro0), datakey(ino, n) ∈ ri0, datakey(ino, n) ∈ ri1, ri0[datakey(ino, n)] ∈ fs0, fo1 ⊆ dom fi1, ro1 ⊆ dom ri1, ro0 ⊆ dom ri0, fo0 ⊆ dom fi0, ∀ key0. ( key0 ∈ ri0 → (key0.inode? → fs0[ri0[key0]].inode? ∧ key0.ino ≠ 0) ∧ ( key0.dentry? → fs0[ri0[key0]].dentry? ∧ inodekey(key0.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key0]].ino) ∈ ri0 ∧ ¬ inodekey(key0.ino) ∈ ro0 ∧ ¬ inodekey(fs0[ri0[key0]].ino) ∈ ro0 ∧ fs0[ri0[inodekey(key0.ino)]].directory) ∧ ( key0.data? → fs0[ri0[key0]].data? ∧ inodekey(key0.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key0.ino)]].directory ∧ # fs0[ri0[key0]].data = VFS_PAGE_SIZE)) → key0 ∈ ri1 → ri1[key0] ∈ fs1 ∧ fs1[ri1[key0]].key = key0 ∧ (key0.inode? → fs1[ri1[key0]].inode? ∧ key0.ino ≠ 0) ∧ ( key0.dentry? → fs1[ri1[key0]].dentry? ∧ inodekey(key0.ino) ∈ ri1 ∧ inodekey(fs1[ri1[key0]].ino) ∈ ri1 ∧ ¬ inodekey(key0.ino) ∈ ro1 ∧ ¬ inodekey(fs1[ri1[key0]].ino) ∈ ro1 ∧ fs1[ri1[inodekey(key0.ino)]].directory) ∧ ( key0.data? → fs1[ri1[key0]].data? ∧ inodekey(key0.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key0.ino)]].directory ∧ # fs1[ri1[key0]].data = VFS_PAGE_SIZE), ∀ adr. ( adr ∈ log0 → (fs0[adr].inode? → fs0[adr].key.inode? ∧ fs0[adr].key.ino ≠ 0) ∧ (fs0[adr].dentry? → fs0[adr].key.dentry?) ∧ (fs0[adr].data? → fs0[adr].key.data?) ∧ (fs0[adr].trunc? → fs0[adr].key.inode?)) → adr ∈ log1 → adr ∈ fs1 ∧ (fs1[adr].inode? → fs1[adr].key.inode? ∧ fs1[adr].key.ino ≠ 0) ∧ (fs1[adr].dentry? → fs1[adr].key.dentry?) ∧ (fs1[adr].data? → fs1[adr].key.data?) ∧ (fs1[adr].trunc? → fs1[adr].key.inode?), ∀ key. key ∈ fo1 → key ∈ fi1, ∀ key. key ∈ ro1 → key ∈ ri1 ⊦ dups(log0), inodekey(0) ∈ ri1, inodekey(0) ∈ ri0, ri1[datakey(ino, n)] ∈ fs1 ∧ fs1[ri1[datakey(ino, n)]].data? ∧ fs1[ri1[datakey(ino, n)]].key = datakey(ino, n), inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory ∧ # fs0[ri0[datakey(ino, n)]].data = VFS_PAGE_SIZE

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: node name: elim-05 seq: ⊦ nd.data? → (key = nd.key ∧ buf = nd.data ↔ nd = datanode(key, buf)) subst: [nd, key, buf] → [fs0[ri0[datakey(ino, n)]], key, buf]

Additional information

Used simplifier rules: ⊦ datanode(key, buf).data?; (s)%⊦ node-closed(datanode(key, buf), ri, fs, ro) ↔ inodekey(key.ino) ∈ ri ∧ ¬ fs[ri[inodekey(key.ino)]].directory ∧ # buf = VFS_PAGE_SIZE; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ nd.data? → (key = nd.key ∧ buf = nd.data ↔ nd = datanode(key, buf)); (elim) Used terms: fs0[ri0[datakey(ino, n)]], key, buf