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Proof step 45 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(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, 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 ⊦ 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, ubifs-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, 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) ], ri0[inodekey(m3), adr1][dentrykey(m3, str0), adr2][inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), adr3], ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, 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) ], ri0[inodekey(m3), adr1][dentrykey(m3, str0), adr2][inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), adr3], ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, 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) ], ri0[inodekey(m3), adr1][dentrykey(m3, str0), adr2][inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), adr3]) ∧ orphans-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, 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) ], ri0[inodekey(m3), adr1][dentrykey(m3, str0), adr2][inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), adr3], ro)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 15

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