[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 79 from proof inv-create (previous step)

fs1[ri1[key]].key = key, key.data?, fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs1, ri1, ro, fi, fo, log0), ri1[key] ∈ fs1, ri1[inodekey(m)] ∈ fs1, inodekey(m) ∈ ri1, key ∈ ri1, inodekey(key.ino) ∈ ri1, key.data? → fs1[ri1[key]].data? ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE, key.dentry? → fs1[ri1[key]].dentry? ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro ∧ fs1[ri1[inodekey(key.ino)]].directory, key.inode? → fs1[ri1[key]].inode?, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ key.ino = 0, 0 = m, adr1 = adr3, adr1 = adr2, adr2 = adr3, inodekey(m) = key, n = 0, inodekey(m) ∈ ro, dentrykey(m, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, fs1[ri1[key]].data? ∧ ¬ (adr3 = (m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]) ⊃ inodenode(inodekey(n), md, false, 1, 0, 0) ;(adr2 = (m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])] ) ) ) .directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
fs1[ri1[datakey(ino, n0)]].key = datakey(ino, n0), fs1[ri1[datakey(ino, n0)]].data?, fs1[ri1[inodekey(m)]].directory, (adr3 = ri1[inodekey(ino)] ⊃ inodenode(inodekey(n), md, false, 1, 0, 0) ;(adr2 = ri1[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = ri1[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1) ;fs1[ri1[inodekey(ino)]] ) ) ) .directory, fs1[ri1[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs1, ri1, ro, fi, fo, log0), ri1[datakey(ino, n0)] ∈ fs1, ri1[inodekey(m)] ∈ fs1, inodekey(m) ∈ ri1, datakey(ino, n0) ∈ ri1, inodekey(ino) ∈ ri1, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ 0 = m, adr1 = adr3, adr1 = adr2, adr2 = adr3, ino = 0, n = 0, fs1[ri1[inodekey(ino)]].directory, inodekey(m) ∈ ro, dentrykey(m, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1

Rule argument

Additional information

Used simplifier rules: elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));%data-ubifs-cons: ⊦ datakey(ino, n) ∈ ri ∧ ri[datakey(ino, n)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[datakey(ino, n)]].data?;%ubifs-file-in: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%ubifs-file-notdir: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ fs[ri[inodekey(ino)]].directory; (forward) from specification aubifs-inv% ⊦ ¬ datakey(m, m0).inode?; (s)% ⊦ ¬ datakey(m, m0).dentry?; (s)%⊦ datakey(m, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → # fs[ri[datakey(m, n)]].data = VFS_PAGE_SIZE; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ datakey(m, m0).ino = m; (s)