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Proof step 77 from proof inv-link (previous step)

fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino0, str)]].ino, fs0[ri0[dentrykey(ino0, str)]].dentry?, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].inode?, fs0[ri0[inodekey(m3)]].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), dentrykey(ino0, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino, str) ∈ ri0, inodekey(ino0) ∈ ri0, inodekey(ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, 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, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ fs0[ri0[dentrykey(ino0, str)]].ino = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].directory, inodekey(ino0) ∈ ro, inodekey(m3) ∈ ro, dentrykey(m3, str0) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ro, inodekey(ino) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, (adr = adr3 ∨ adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .inode? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .key .inode? ∧ (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .key .ino ≠ 0) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .dentry? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .key .dentry?) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .data? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .key .data?) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .trunc? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .key .inode?)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 78:
fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino0, str)]].ino, fs0[ri0[dentrykey(ino0, str)]].dentry?, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(m3)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].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(m3)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)] ∈ fs0, inodekey(ino) ∈ ri0, inodekey(ino0) ∈ ri0, dentrykey(ino, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(ino0, str) ∈ 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?), fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, adr ∈ log0 ∨ adr = adr1 ∨ adr = adr2 ∨ adr = adr3 ⊦ fs0[ri0[dentrykey(ino0, str)]].ino = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(ino) ∈ ro, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ro, dentrykey(m3, str0) ∈ ri0, inodekey(m3) ∈ ro, inodekey(ino0) ∈ ro, adr ∈ log0, (adr = adr3 ∨ adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .inode? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .key .inode? ∧ (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .key .ino ≠ 0) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .dentry? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .key .dentry?) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .data? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .key .data?) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .trunc? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = adr ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = adr ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[adr] ) ) ) .key .inode?)

Rule argument

fma: adr ∈ log0

Additional information

Used formulas: adr ∈ log0