Proof step 317 from proof inv-truncate (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 318:

  fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf), fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data?, fs0[ri0[inodekey(m0)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, m4 ≤ n1 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, adr3 ∈ ri0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, (ro ⊆ dom ri0 → key ∈ ro → ¬ key ∈ ri0 ∨ ¬ key.data? ∨ key.ino ≠ m0 ∨ ¬ m4 ≤ key.part * VFS_PAGE_SIZE) ∧ ( ri0[key0] ∈ fs0 ∧ (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) ∈ ro ∧ ¬ inodekey(fs0[ri0[key0]].ino) ∈ ro ∧ 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 ∈ ri0 ∧ (¬ key0.data? ∨ key0.ino ≠ m0 ∨ ¬ m4 ≤ key0.part * VFS_PAGE_SIZE) → ( (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) = adr3 ∨ (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) = adr2 ∨ (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) = adr1 ∨ (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ∈ fs0) ∧ ( adr3 = (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;( adr2 = (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;( adr1 = (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ truncnode(inodekey(m0), m4) ;fs0 [(key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ] ) ) ) .key = key0 ∧ ( key0.inode? → (adr3 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .inode? ∧ key0.ino ≠ 0) ∧ ( key0.dentry? → (adr3 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .dentry? ∧ inodekey(key0.ino) ∈ ri0 ∧ ( (adr3 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .ino = m0 ∨ inodekey ((adr3 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key0.ino) ∈ ro ∧ ¬ inodekey ((adr3 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .ino) ∈ ro ∧ (adr3 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ truncnode(inodekey(m0), m4) ;fs0[(m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)])] ) ) ) .directory) ∧ ( key0.data? → ( adr3 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;( adr2 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;( adr1 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ truncnode(inodekey(m0), m4) ;fs0 [(key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ] ) ) ) .data? ∧ inodekey(key0.ino) ∈ ri0 ∧ ¬ (adr3 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ truncnode(inodekey(m0), m4) ;fs0[(m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)])] ) ) ) .directory ∧ # ( adr3 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;( adr2 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;( adr1 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ truncnode(inodekey(m0), m4) ;fs0 [(key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ] ) ) ) .data = VFS_PAGE_SIZE)) ∧ ( ( adr ∈ log0 → adr ∈ fs0 ∧ (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 ∈ log0 ∨ adr = adr1 ∨ adr = adr2 ∨ adr = adr3 → (adr = adr3 ∨ adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr3 = adr ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) ) .inode? → (adr3 = adr ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) ) .key .inode? ∧ (adr3 = adr ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) ) .key .ino ≠ 0) ∧ ( (adr3 = adr ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) ) .dentry? → (adr3 = adr ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) ) .key .dentry?) ∧ ( (adr3 = adr ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) ) .data? → (adr3 = adr ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) ) .key .data?) ∧ ( (adr3 = adr ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) ) .trunc? → (adr3 = adr ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ;(adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) ) .key .inode?))

Rule argument

Additional information

Used simplifier rules: ubifs-cons-reduce: ⊦ ubifs-cons(fs0, ri0, ro0, fi0, fo0, log0) → ( ubifs-cons(fs1, ri1, ro1, fi1, fo1, log1) ↔ ¬ inodekey(0) ∈ ri1 ∧ (ro0.inodes? → ro1.inodes?) ∧ (fo0.inodes? → fo1.inodes?) ∧ (ro0 ⊆ dom ri0 → (∀ key. key ∈ ro1 → key ∈ ri1)) ∧ (fo0 ⊆ dom fi0 → (∀ key. key ∈ fo1 → key ∈ fi1)) ∧ (¬ dups(log0) → ¬ dups(log1)) ∧ (∀ key. ( 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 ∈ 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 → adr ∈ fs0 ∧ ( 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?)));%in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-diff-ri: ⊦ (ri \ ks)[key] = (key ∈ ks ⊃ (∅)[key];ri[key]);%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ adr ∈ ax + ax0 ↔ adr ∈ ax ∨ adr ∈ ax0; (s)% ⊦ ¬ inodekey(m).data?; (s)% ⊦ key.dentry? → ¬ key.data?; (s)% ⊦ key.inode? → ¬ key.data?; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ ri-cons(ri, fs) ∧ key ∈ ri → fs[ri[key]].key = key; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ ¬ adr0 ∈ fs ∧ ¬ adr1 ∈ fs ∧ ¬ adr2 ∈ fs ∧ adr0 ≠ adr1 ∧ adr0 ≠ adr2 ∧ adr1 ≠ adr2 → ¬ dups(log + adr0 ' + adr1 ' + adr2 '); (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ dups(log); (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ fo → key ∈ fi; (ss)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ datakeys(key, ri[inodekey(ino), adr]) = datakeys(key, ri); (s)%⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ ro → key ∈ ri; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ inodekey(0) ∈ ri; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)