Proof step 51 from proof inv-mkdir (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 52:

  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[inodekey(m)] ∈ fs1, inodekey(m) ∈ ri1, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ 0 = m, adr1 = adr3, adr1 = adr2, adr2 = adr3, n = 0, inodekey(m) ∈ ro, dentrykey(m, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, ( ( adr ∈ log0 → adr ∈ fs1 ∧ (fs1[adr].inode? → fs1[adr].key.inode? ∧ fs1[adr].key.ino ≠ 0) ∧ (fs1[adr].dentry? → fs1[adr].key.dentry?) ∧ (fs1[adr].data? → fs1[adr].key.data?) ∧ (fs1[adr].trunc? → fs1[adr].key.inode?)) → adr ∈ log0 ∨ adr = adr1 ∨ adr = adr2 ∨ adr = adr3 → (adr = adr3 ∨ adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs1) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = adr ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[adr] ) ) ) .inode? → (adr3 = adr ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = adr ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[adr] ) ) ) .key .inode? ∧ (adr3 = adr ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = adr ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[adr] ) ) ) .key .ino ≠ 0) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = adr ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[adr] ) ) ) .dentry? → (adr3 = adr ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = adr ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[adr] ) ) ) .key .dentry?) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = adr ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[adr] ) ) ) .data? → (adr3 = adr ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = adr ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[adr] ) ) ) .key .data?) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = adr ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[adr] ) ) ) .trunc? → (adr3 = adr ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = adr ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[adr] ) ) ) .key .inode?)) ∧ ( ( key ∈ ri1 → ri1[key] ∈ fs1 ∧ fs1[ri1[key]].key = key ∧ (key.inode? → fs1[ri1[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs1[ri1[key]].dentry? ∧ inodekey(key.ino) ∈ ri1 ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro ∧ fs1[ri1[inodekey(key.ino)]].directory) ∧ ( key.data? → fs1[ri1[key]].data? ∧ inodekey(key.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE)) → key = inodekey(n) ∨ key = dentrykey(m, str) ∨ key ∈ ri1 → ( (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) = adr3 ∨ (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) = adr2 ∨ (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) = adr1 ∨ (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ∈ fs1) ∧ (adr3 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key])))] ) ) ) .key = key ∧ ( key.inode? → (adr3 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key])))] ) ) ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr3 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key])))] ) ) ) .dentry? ∧ (key.ino = n ∨ inodekey(key.ino) ∈ ri1) ∧ ( (adr3 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode (inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key])))] ) ) ) .ino = n ∨ (adr3 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode (inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key])))] ) ) ) .ino = m ∨ inodekey ((adr3 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode (inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key])))] ) ) ) .ino) ∈ ri1) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr3 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode (inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key])))] ) ) ) .ino) ∈ ro ∧ (adr3 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]))] ) ) ) .directory) ∧ ( key.data? → (adr3 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key])))] ) ) ) .data? ∧ (key.ino = n ∨ inodekey(key.ino) ∈ ri1) ∧ ¬ (adr3 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]))] ) ) ) .directory ∧ # (adr3 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key]))) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(n) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ adr2;(inodekey(m) = key ⊃ adr1;ri1[key])))] ) ) ) .data = VFS_PAGE_SIZE))

Rule argument

Additional information

Used simplifier rules: ubifs-cons-reduce: ⊦ ubifs-cons(fs0, ri0, ro0, fi0, fo0, log0) → ( ubifs-cons(fs1, ri1, ro1, fi1, fo1, log1) ↔ ¬ inodekey(0) ∈ ri1 ∧ (ro0.inodes? → ro1.inodes?) ∧ (fo0.inodes? → fo1.inodes?) ∧ (ro0 ⊆ dom ri0 → (∀ key. key ∈ ro1 → key ∈ ri1)) ∧ (fo0 ⊆ dom fi0 → (∀ key. key ∈ fo1 → key ∈ fi1)) ∧ (¬ dups(log0) → ¬ dups(log1)) ∧ (∀ key. ( key ∈ ri0 → ri0[key] ∈ fs0 ∧ fs0[ri0[key]].key = key ∧ (key.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro0 ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro0 ∧ fs0[ri0[inodekey(key.ino)]].directory) ∧ ( key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE)) → key ∈ ri1 → ri1[key] ∈ fs1 ∧ fs1[ri1[key]].key = key ∧ (key.inode? → fs1[ri1[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs1[ri1[key]].dentry? ∧ inodekey(key.ino) ∈ ri1 ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro1 ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro1 ∧ fs1[ri1[inodekey(key.ino)]].directory) ∧ ( key.data? → fs1[ri1[key]].data? ∧ inodekey(key.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE)) ∧ (∀ adr. ( 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 ∈ log1 → adr ∈ fs1 ∧ ( fs1[adr].inode? → fs1[adr].key.inode? ∧ fs1[adr].key.ino ≠ 0) ∧ (fs1[adr].dentry? → fs1[adr].key.dentry?) ∧ (fs1[adr].data? → fs1[adr].key.data?) ∧ (fs1[adr].trunc? → fs1[adr].key.inode?)));%in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ adr ∈ ax + ax0 ↔ adr ∈ ax ∨ adr ∈ ax0; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ ¬ adr0 ∈ fs ∧ ¬ adr1 ∈ fs ∧ ¬ adr2 ∈ fs ∧ adr0 ≠ adr1 ∧ adr0 ≠ adr2 ∧ adr1 ≠ adr2 → ¬ dups(log + adr0 ' + adr1 ' + adr2 '); (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ dups(log); (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ fo → key ∈ fi; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ ro → key ∈ ri; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ inodekey(0) ∈ ri; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)