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Proof step 607 from proof inv-truncate (previous step)

fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, fs0[ri0[inodekey(m0)]].inode?, fo.inodes?, ro.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(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, m4 ≤ n0, ro ⊆ dom ri0, 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 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, (adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .inode? → (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .key .inode? ∧ (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .key .ino ≠ 0) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .dentry? → (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .key .dentry?) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .data? → (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .key .data?) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .trunc? → (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .key .inode?)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 608:
fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, fs0[ri0[inodekey(m0)]].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), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, m4 ≤ n0, ro ⊆ dom ri0, 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 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, adr2 ∈ fs0, adr1 ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, adr ∈ log0, (adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .inode? → (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .key .inode? ∧ (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .key .ino ≠ 0) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .dentry? → (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .key .dentry?) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .data? → (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .key .data?) ∧ ( (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .trunc? → (adr2 = adr ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = adr ⊃ truncnode(inodekey(m0), m4);fs0[adr]) ) .key .inode?)

Rule argument

fma: adr ∈ log0

Additional information

Used formulas: adr ∈ log0