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Proof step 64 from proof ubifs-cons-reduce (previous step)

fo0.inodes?, ro0.inodes?, key-cons(key, fs0[ri0[key]]), log-cons(log1, fs1), log-cons(log0, fs0), ri-cons(ri1, fs1), ri0[key] ∈ fs0, key ∈ ri1, key ∈ ri0, fo0 ⊆ dom fi0, ro0 ⊆ dom ri0, ro1 ⊆ dom ri1, fo1 ⊆ dom fi1, ∀ key. key ∈ ro1 → key ∈ ri1, ∀ key. key ∈ fo1 → key ∈ fi1, ∀ 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 ∈ ri0 → ri0[key] ∈ fs0 ∧ node-closed(fs0[ri0[key]], ri0, fs0, ro0) ⊦ dups(log0), node-closed(fs1[ri1[key]], ri1, fs1, ro1), inodekey(0) ∈ ri0, inodekey(0) ∈ ri1, (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)

User applied rule all left

And obtained the following new goals

Proof step 65:
ro0.inodes?, fo0.inodes?, key-cons(key, fs0[ri0[key]]), log-cons(log0, fs0), log-cons(log1, fs1), ri-cons(ri1, fs1), key ∈ ri0, key ∈ ri1, ri0[key] ∈ fs0, fo1 ⊆ dom fi1, ro1 ⊆ dom ri1, ro0 ⊆ dom ri0, fo0 ⊆ dom fi0, key ∈ ri0 → ri0[key] ∈ fs0 ∧ node-closed(fs0[ri0[key]], ri0, fs0, ro0), ∀ 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), node-closed(fs1[ri1[key]], ri1, fs1, ro1), inodekey(0) ∈ ri1, inodekey(0) ∈ ri0, (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)

Rule argument

pos: left 17 terms: key abort: F discard: T computed: T

Additional information

Used terms: key