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Proof step 745 from proof inv-truncate (previous step)

fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, fs0[ri0[inodekey(m)]].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), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, ro ⊆ dom ri0, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ adr1 = adr2, m = 0, fs0[ri0[inodekey(m)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, (ro ⊆ dom ri0 → key ∈ ro → ¬ key ∈ ri0 ∨ ¬ key.data? ∨ key.ino ≠ m ∨ ¬ min(n0, m3) ≤ 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 ≠ m ∨ ¬ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE) → ( (key0.data? ∧ key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0])) = adr2 ∨ (key0.data? ∧ key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0])) = adr1 ∨ (key0.data? ∧ key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0])) ∈ fs0) ∧ (adr2 = (key0.data? ∧ key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0])) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = (key0.data? ∧ key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0])) ⊃ truncnode(inodekey(m), min(n0, m3)) ;fs0[(key0.data? ∧ key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0]))] ) ) .key = key0 ∧ ( key0.inode? → (adr2 = (inodekey(m) = key0 ⊃ adr2;ri0[key0]) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = (inodekey(m) = key0 ⊃ adr2;ri0[key0]) ⊃ truncnode(inodekey(m), min(n0, m3));fs0[(inodekey(m) = key0 ⊃ adr2;ri0[key0])]) ) .inode? ∧ key0.ino ≠ 0) ∧ ( key0.dentry? → (adr2 = (inodekey(m) = key0 ⊃ adr2;ri0[key0]) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = (inodekey(m) = key0 ⊃ adr2;ri0[key0]) ⊃ truncnode(inodekey(m), min(n0, m3));fs0[(inodekey(m) = key0 ⊃ adr2;ri0[key0])]) ) .dentry? ∧ inodekey(key0.ino) ∈ ri0 ∧ ( (adr2 = (inodekey(m) = key0 ⊃ adr2;ri0[key0]) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = (inodekey(m) = key0 ⊃ adr2;ri0[key0]) ⊃ truncnode(inodekey(m), min(n0, m3));fs0[(inodekey(m) = key0 ⊃ adr2;ri0[key0])]) ) .ino = m ∨ inodekey ((adr2 = (inodekey(m) = key0 ⊃ adr2;ri0[key0]) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = (inodekey(m) = key0 ⊃ adr2;ri0[key0]) ⊃ truncnode(inodekey(m), min(n0, m3));fs0[(inodekey(m) = key0 ⊃ adr2;ri0[key0])]) ) .ino) ∈ ri0) ∧ ¬ inodekey(key0.ino) ∈ ro ∧ ¬ inodekey ((adr2 = (inodekey(m) = key0 ⊃ adr2;ri0[key0]) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = (inodekey(m) = key0 ⊃ adr2;ri0[key0]) ⊃ truncnode(inodekey(m), min(n0, m3));fs0[(inodekey(m) = key0 ⊃ adr2;ri0[key0])]) ) .ino) ∈ ro ∧ (adr2 = (m = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = (m = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ truncnode(inodekey(m), min(n0, m3)) ;fs0[(m = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)])] ) ) .directory) ∧ ( key0.data? → (adr2 = (key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0])) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = (key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0])) ⊃ truncnode(inodekey(m), min(n0, m3)) ;fs0[(key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0]))] ) ) .data? ∧ inodekey(key0.ino) ∈ ri0 ∧ ¬ (adr2 = (m = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = (m = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ truncnode(inodekey(m), min(n0, m3)) ;fs0[(m = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)])] ) ) .directory ∧ # (adr2 = (key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0])) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = (key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;ri0[key0])) ⊃ truncnode(inodekey(m), min(n0, m3)) ;fs0[(key0.ino = m ∧ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(inodekey(m) = key0 ⊃ adr2;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 = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m), min(n0, m3));fs0[adr]) ) .inode? → (adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m), min(n0, m3));fs0[adr]) ) .key .inode? ∧ (adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m), min(n0, m3));fs0[adr]) ) .key .ino ≠ 0) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m), min(n0, m3));fs0[adr]) ) .dentry? → (adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m), min(n0, m3));fs0[adr]) ) .key .dentry?) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m), min(n0, m3));fs0[adr]) ) .data? → (adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m), min(n0, m3));fs0[adr]) ) .key .data?) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m), min(n0, m3));fs0[adr]) ) .trunc? → (adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m), min(n0, m3));fs0[adr]) ) .key .inode?)), m3 ≤ n0 ∧ m3 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information