[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 34 from proof inv-write-inode (previous step)

fs0[ri[key]].key = key, fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, fs0[ri[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), key ∈ ri, ri[key] ∈ fs0, ri[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, key.inode? → fs0[ri[key]].inode? ∧ key.ino ≠ 0, key.dentry? → fs0[ri[key]].dentry? ∧ inodekey(key.ino) ∈ ri ∧ inodekey(fs0[ri[key]].ino) ∈ ri ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri[key]].ino) ∈ ro ∧ fs0[ri[inodekey(key.ino)]].directory, key.data? → fs0[ri[key]].data? ∧ inodekey(key.ino) ∈ ri ∧ ¬ fs0[ri[inodekey(key.ino)]].directory ∧ # fs0[ri[key]].data = VFS_PAGE_SIZE, ¬ fs0[ri[inodekey(m)]].directory ∧ ¬ boolvar0 ∨ fs0[ri[inodekey(m)]].directory ∧ boolvar0 ∧ m2 = fs0[ri[inodekey(m)]].size ⊦ 0 = m, adr1 ∈ fs0, ((inodekey(m) = key ⊃ adr1;ri[key]) = adr1 ∨ (inodekey(m) = key ⊃ adr1;ri[key]) ∈ fs0) ∧ (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .key = key ∧ ( key.inode? → (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .dentry? ∧ inodekey(key.ino) ∈ ri ∧ ( (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .ino = m ∨ inodekey ((adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .ino) ∈ ri) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .ino) ∈ ro ∧ (adr1 = (m = key.ino ⊃ adr1;ri[inodekey(key.ino)]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(m = key.ino ⊃ adr1;ri[inodekey(key.ino)])] ) .directory) ∧ ( key.data? → (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .data? ∧ inodekey(key.ino) ∈ ri ∧ ¬ (adr1 = (m = key.ino ⊃ adr1;ri[inodekey(key.ino)]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(m = key.ino ⊃ adr1;ri[inodekey(key.ino)])] ) .directory ∧ # (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .data = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 35:
fs0[ri[key]].key = key, fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, fs0[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, ri[key] ∈ fs0, key ∈ ri, key.data? → fs0[ri[key]].data? ∧ inodekey(key.ino) ∈ ri ∧ ¬ fs0[ri[inodekey(key.ino)]].directory ∧ # fs0[ri[key]].data = VFS_PAGE_SIZE, key.dentry? → fs0[ri[key]].dentry? ∧ inodekey(key.ino) ∈ ri ∧ inodekey(fs0[ri[key]].ino) ∈ ri ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri[key]].ino) ∈ ro ∧ fs0[ri[inodekey(key.ino)]].directory, key.inode? → fs0[ri[key]].inode? ∧ key.ino ≠ 0, ¬ fs0[ri[inodekey(m)]].directory ∧ ¬ boolvar0 ∨ fs0[ri[inodekey(m)]].directory ∧ boolvar0 ∧ m2 = fs0[ri[inodekey(m)]].size ⊦ (inodekey(m) = key ⊃ adr1;ri[key]) = adr1, 0 = m, adr1 ∈ fs0, ((inodekey(m) = key ⊃ adr1;ri[key]) = adr1 ∨ (inodekey(m) = key ⊃ adr1;ri[key]) ∈ fs0) ∧ (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .key = key ∧ ( key.inode? → (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .dentry? ∧ inodekey(key.ino) ∈ ri ∧ ( (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .ino = m ∨ inodekey ((adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .ino) ∈ ri) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .ino) ∈ ro ∧ (adr1 = (m = key.ino ⊃ adr1;ri[inodekey(key.ino)]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(m = key.ino ⊃ adr1;ri[inodekey(key.ino)])] ) .directory) ∧ ( key.data? → (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .data? ∧ inodekey(key.ino) ∈ ri ∧ ¬ (adr1 = (m = key.ino ⊃ adr1;ri[inodekey(key.ino)]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(m = key.ino ⊃ adr1;ri[inodekey(key.ino)])] ) .directory ∧ # (adr1 = (inodekey(m) = key ⊃ adr1;ri[key]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(inodekey(m) = key ⊃ adr1;ri[key])] ) .data = VFS_PAGE_SIZE)

Rule argument

fma: (inodekey(m) = key ⊃ adr1;ri[key]) = adr1

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ ¬ inodekey(m).dentry?; (s)% ⊦ ¬ inodekey(m).data?; (s) Used formulas: (inodekey(m) = key ⊃ adr1;ri[key]) = adr1