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Proof step 143 from proof ubifs-cons-reduce (previous step)

ubifs-cons(fs0, ri0, ro0, fi0, fo0, log0), adr ∈ fs1, adr ∈ log1, ro1 ⊆ dom ri1, fo1 ⊆ dom fi1, fs1[adr].trunc? → fs1[adr].key.inode?, fs1[adr].data? → fs1[adr].key.data?, fs1[adr].dentry? → fs1[adr].key.dentry?, fs1[adr].inode? → fs1[adr].key.inode? ∧ fs1[adr].key.ino ≠ 0, ∀ key. key ∈ ro1 → key ∈ ri1, ∀ key. key ∈ fo1 → key ∈ fi1, ∀ key. ( key ∈ ri0 → 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 ∈ ri1 → ri1[key] ∈ fs1 ∧ fs1[ri1[key]].key = key ∧ (key.inode? → fs1[ri1[key]].inode? ∧ key.ino ≠ 0) ∧ ( 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) ⊦ node-cons(fs1[adr].key, fs1[adr]), inodekey(0) ∈ ri1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-inv name: node-cons seq: ⊦ node-cons(key, nd) ↔ (nd.inode? → key.inode? ∧ key.ino ≠ 0) ∧ (nd.dentry? → key.dentry?) ∧ (nd.data? → key.data?) ∧ (nd.trunc? → key.inode?) subst: [nd, key] → [fs1[adr], fs1[adr].key] flags: <all paths>

Additional information

Used terms: fs1[adr], fs1[adr].key