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Proof step 109 from proof inv-link (previous step)

fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino0, str)]].ino, replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, 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), key-cons(key, fs0[ri0[key]]), log-cons (log0, fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)]), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), 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)], ri0[inodekey(m3), adr1], ro, fi, fo, log0 + adr1 '), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-cons (ri0[inodekey(m3), adr1], fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)]), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), key ∈ ri0, 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, ri0[key] ∈ fs0, 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, adr3 ∈ fs0, adr2 ∈ fs0, replay-safe (log0, 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) ], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, 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) ], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, 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) ], fi ⊖ fo) [inodekey(m3), adr1 ] ∧ ¬ adr3 ∈ replay-log (log0, 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) ], fi ⊖ fo) [inodekey(m3), adr1 ] [dentrykey(m3, str0), adr2 ] ∧ replay-log (log0, 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) ], fi ⊖ fo) [inodekey(m3), adr1 ] [dentrykey(m3, str0), adr2 ] [inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), adr3 ] = ri0[inodekey(m3), adr1][dentrykey(m3, str0), adr2][inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), adr3] ⊖ ro, ( (adr = adr1 ∨ adr ∈ fs0) ∧ node-cons ((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, (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] )) → adr ∈ log0 → node-cons ((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, (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] ) ))) ∧ ( (key0 ∈ ri0 → ri0[key0] ∈ fs0 ∧ key-cons(key0, fs0[ri0[key0]])) → key0 = dentrykey(m3, str0) ∨ key0 ∈ ri0 → ( (dentrykey(m3, str0) = key0 ⊃ adr2;(inodekey(m3) = key0 ⊃ adr1;ri0[key0])) = adr2 ∨ (dentrykey(m3, str0) = key0 ⊃ adr2;(inodekey(m3) = key0 ⊃ adr1;ri0[key0])) = adr1 ∨ (dentrykey(m3, str0) = key0 ⊃ adr2;(inodekey(m3) = key0 ⊃ adr1;ri0[key0])) ∈ fs0) ∧ key-cons (key0, (adr2 = (dentrykey(m3, str0) = key0 ⊃ adr2;(inodekey(m3) = key0 ⊃ adr1;ri0[key0])) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (dentrykey(m3, str0) = key0 ⊃ adr2;(inodekey(m3) = key0 ⊃ adr1;ri0[key0])) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(dentrykey(m3, str0) = key0 ⊃ adr2;(inodekey(m3) = key0 ⊃ adr1;ri0[key0]))] ) ))), ((inodekey(m3) = key ⊃ adr1;ri0[key]) = adr2 ∨ (inodekey(m3) = key ⊃ adr1;ri0[key]) = adr1 ∨ (inodekey(m3) = key ⊃ adr1;ri0[key]) ∈ fs0) ∧ key-cons (key, (adr2 = (inodekey(m3) = key ⊃ adr1;ri0[key]) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (inodekey(m3) = key ⊃ adr1;ri0[key]) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(m3) = key ⊃ adr1;ri0[key])] ) ))

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: inodekey(m3) = key

Additional information

Used simplifier rules: ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → key-cons(key, fs[ri[key]]); (ss)%⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0; (s)% ⊦ ri-cons(ri, fs) ∧ key ∈ ri → fs[ri[key]].key = key; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s) Used formulas: inodekey(m3) = key