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Proof step 38 from proof ubifs-cons-reduce (previous step)

fo1.inodes?, ro1.inodes?, ubifs-cons(fs0, ri0, ro0, fi0, fo0, log0), ∀ 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 → 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), ∀ key. key ∈ fo1 → key ∈ fi1, ∀ key. key ∈ ro1 → key ∈ ri1 ⊦ dups(log1), ubifs-cons(fs1, ri1, ro1, fi1, fo1, log1), inodekey(0) ∈ ri1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ↔ ¬ inodekey(0) ∈ ri ∧ ri-cons(ri, fs) ∧ log-cons(log, fs) ∧ ¬ dups(log) ∧ ri-closed(ri, fs, ro) ∧ ro.inodes? ∧ fo.inodes? ∧ ro ⊆ dom ri ∧ fo ⊆ dom fi
Proof step 40:
ro1.inodes?, fo1.inodes?, ubifs-cons(fs0, ri0, ro0, fi0, fo0, log0), ∀ 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), ∀ 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?) ⊦ dups(log1), inodekey(0) ∈ ri1, ¬ inodekey(0) ∈ ri1 ∧ ri-cons(ri1, fs1) ∧ log-cons(log1, fs1) ∧ ¬ dups(log1) ∧ ri-closed(ri1, fs1, ro1) ∧ ro1.inodes? ∧ fo1.inodes? ∧ ro1 ⊆ dom ri1 ∧ fo1 ⊆ dom fi1

Rule argument

spec: aubifs-inv name: ubifs-cons seq: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ↔ ¬ inodekey(0) ∈ ri ∧ ri-cons(ri, fs) ∧ log-cons(log, fs) ∧ ¬ dups(log) ∧ ri-closed(ri, fs, ro) ∧ ro.inodes? ∧ fo.inodes? ∧ ro ⊆ dom ri ∧ fo ⊆ dom fi subst: [log, fo, fi, ro, ri, fs] → [log1, fo1, fi1, ro1, ri1, fs1] flags: <all paths>

Additional information

Used terms: log1, fo1, fi1, ro1, ri1, fs1