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Proof step 319 from proof inv-truncate (previous step)

fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(buf0, 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)]] = datanode(key1, buf0), fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data?, fs0[ri0[inodekey(m0)]].inode?, ro.inodes?, fo.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(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, m4 ≤ n1 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr3 ∈ ri0, (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?))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 320:
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)]] = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf0), 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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;( 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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;( 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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;( 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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(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: ⊦ datanode(key, buf).data?; (s)% ⊦ datanode(key, buf) = datanode(key0, buf0) ↔ key = key0 ∧ buf = buf0; (ws)% ⊦ datanode(key, buf).data:= buf0 = datanode(key, buf0); (s)