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Proof step 90 from proof inv-rmdir (previous step)

1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nlink, dentrykeys(inodekey(fs0[ri0[dentrykey(m0, str)]].ino), ri0) = ∅, links(fs0[ri0[dentrykey(m0, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m0, str), fs0[ri0[dentrykey(m0, str)]].dentry?, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].inode?, 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), dentrykey(m0, str) ∈ ri0, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, 1 ≤ fs0[ri0[inodekey(m0)]].size, 1 ≤ fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, adr = adr2 ∨ adr = adr3 ⊦ fs0[ri0[dentrykey(m0, str)]].ino = 0, fs0[ri0[dentrykey(m0, str)]].ino = ROOT_INO, fs0[ri0[inodekey(m0)]].nsubdirs = 0, fs0[ri0[inodekey(m0)]].size = 0, adr = adr1, adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, adr ∈ log0, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ro, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, (adr = adr3 ∨ adr = adr2 ∨ adr ∈ fs0) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str), 0);fs0[adr]) ) .inode? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str), 0);fs0[adr]) ) .key .inode? ∧ (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str), 0);fs0[adr]) ) .key .ino ≠ 0) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str), 0);fs0[adr]) ) .dentry? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str), 0);fs0[adr]) ) .key .dentry?) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str), 0);fs0[adr]) ) .data? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str), 0);fs0[adr]) ) .key .data?) ∧ ( (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str), 0);fs0[adr]) ) .trunc? → (adr3 = adr ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str), 0);fs0[adr]) ) .key .inode?)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: adr = adr2

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ ¬ inodenode(key, md, boolvar, m, m0, m1).dentry?; (s)% ⊦ ¬ inodenode(key, md, boolvar, m, m0, m1).data?; (s)% ⊦ ¬ inodenode(key, md, boolvar, m, m0, m1).trunc?; (s)% ⊦ ¬ dentrynode(key, m).inode?; (s)% ⊦ dentrynode(key, m).dentry?; (s)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ ¬ dentrynode(key, m).data?; (s)% ⊦ ¬ dentrynode(key, m).trunc?; (s) Used formulas: adr = adr2