[Imprint][Data Privacy Statement][E-Mail]



View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 752 from proof inv-truncate (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information