Proof step 213 from proof inv-unlink (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 214:

  m3 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(m1)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].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(m1)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, dentrykey(m1, str) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m1)]].size, fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m1 = 0, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, inodekey(m1) ∈ ro, ( ( key ∈ ri0 → ri0[key] ∈ fs0 ∧ (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) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ 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 = inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∨ key ≠ dentrykey(m1, str) ∧ key ∈ ri0 → ( (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) = adr3 ∨ (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) = adr2 ∨ (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) = adr1 ∨ (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ∈ fs0) ∧ ( adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ dentrynode(dentrykey(m1, str), 0) ;( adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ] ) ) ) .key = key ∧ ( key.inode? → ( adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ dentrynode(dentrykey(m1, str), 0) ;( adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ] ) ) ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → ( adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ dentrynode(dentrykey(m1, str), 0) ;( adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ] ) ) ) .dentry? ∧ (key.ino = fs0[ri0[dentrykey(m1, str)]].ino ∨ inodekey(key.ino) ∈ ri0) ∧ ( ( adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ dentrynode(dentrykey(m1, str), 0) ;( adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ] ) ) ) .ino = fs0[ri0[dentrykey(m1, str)]].ino ∨ ( adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ dentrynode(dentrykey(m1, str), 0) ;( adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ] ) ) ) .ino = m1 ∨ inodekey (( adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ dentrynode(dentrykey(m1, str), 0) ;( adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ] ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey (( adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ dentrynode(dentrykey(m1, str), 0) ;( adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ] ) ) ) .ino) ∈ ro ∧ (adr3 = (fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]))] ) ) ) .directory) ∧ ( key.data? → ( adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ dentrynode(dentrykey(m1, str), 0) ;( adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ] ) ) ) .data? ∧ (key.ino = fs0[ri0[dentrykey(m1, str)]].ino ∨ inodekey(key.ino) ∈ ri0) ∧ ¬ (adr3 = (fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]))] ) ) ) .directory ∧ # ( adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ dentrynode(dentrykey(m1, str), 0) ;( adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3 ;(dentrykey(m1, str) = key ⊃ (∅)[dentrykey(m1, str)];(inodekey(m1) = key ⊃ adr1;ri0[key])) ) ] ) ) ) .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 = adr3 → (adr = adr3 ∨ adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = adr ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[adr] ) ) ) .inode? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = adr ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[adr] ) ) ) .key .inode? ∧ (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = adr ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[adr] ) ) ) .key .ino ≠ 0) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = adr ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[adr] ) ) ) .dentry? → (adr3 = adr ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = adr ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[adr] ) ) ) .key .dentry?) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = adr ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[adr] ) ) ) .data? → (adr3 = adr ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = adr ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[adr] ) ) ) .key .data?) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = adr ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[adr] ) ) ) .trunc? → (adr3 = adr ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = adr ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[adr] ) ) ) .key .inode?))

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-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];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)% ⊦ ri-cons(ri, fs) ∧ key ∈ ri → fs[ri[key]].key = key; (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)% ⊦ ks.inodes? → ¬ dentrykey(ino, str) ∈ ks; (s)% ⊦ 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)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)